Unsteady Interaction Research Articles

Experimental Investigation of Additional Loss Associated With Incoming Wakes in Low-Pressure Turbine Cascades

Abstract The present paper aims to experimentally investigate the influence of wake-passing frequency, Reynolds number, and suction surface diffusion rate on the additional loss due to incoming wakes to the profile loss in the low-pressure turbine (LPT) cascades and discuss a design guide for reducing the additional loss. Using a moving-bar mechanism, the unsteady effects of incoming wakes were measured in a low-speed linear turbine cascade facility. The wake-passing frequency was varied by adjusting the moving-bar speed. The different airfoils with different surface velocity distributions were tested to examine the effect of suction surface diffusion rate. For each test case in an unsteady flow condition, the additional loss due to incoming wakes was derived by subtracting the profile loss from the measured total pressure loss across the cascade. Here, the profile loss was estimated by using the friction drag force, which was calculated by the measured surface velocity distribution, and the pressure drag force, which was calculated by the measured surface pressure distribution and the predicted base pressure. The resultant additional loss includes all kinds of losses associated with incoming wakes, such as mixing loss of incoming wakes enhanced in the blade passage and unsteady interaction loss between incoming wakes and surface boundary layers. It was demonstrated that in an unsteady flow condition, a substantial performance improvement was obtained in the entire Reynolds number range by applying the surface velocity distribution with no laminar separation to a low-solidity blade row.

Unsteady interaction and dynamic stability analysis of a two-stage-to-orbit vehicle during transverse stage separation

Hypersonic stage separation is a significant process for the future two-stage-to-orbit (TSTO) vehicle. Strong and complex interstage aerodynamic interference may result in drastic aerodynamic forces and moments, potentially conflicting with the safe separation. Therefore, the dynamic stability of the vehicle during separation is critical to aerospace safety. In this study, numerical analysis of a hypersonic flow with Ma = 6.7 past a parallel-staged TSTO vehicle during stage separation is performed by laminar flow simulations. The TSTO vehicle consists of a wave-rider and a spaceplane as booster and orbiter, respectively. Considering the different centers of gravity for the orbiter during separation, the longitudinal dynamic stability of the orbiter is analyzed based on the dynamic characteristic of the center of pressure (CoP) in different cases. The dynamic separation behavior, aerodynamic characteristics, and typical flowfield patterns are clarified. Moreover, the derivative of CoP to time is proposed and analyzed in detail, which serves as an indicator to determine the dynamic stability and the safe stage separation. A safety separation judgment criterion is also proposed based on the CoP dynamic characteristics for the TSTO vehicle, and the mechanism of CoP variations associated with the unsteady aerodynamic interference during stage separation is revealed.

Experimental and numerical investigation on the unsteady interaction in longitudinal stage separation for parallel-staged two-body configuration

Hypersonic stage separation is a significant process, probably involving complex aerodynamic interaction, which determines the survival of two-stage-to-orbit (TSTO) vehicles. The longitudinal stage separation (LSS) scheme is proposed to improve the safety of the parallel-staged TSTO vehicle, where a small interstage gap may result in weak interference. Therefore, an experimental and numerical study of LSS for the parallel-staged TSTO vehicle at Mach 7 with different angles of attack (AoA) is carried out. The dynamic interaction, including variations in the shock structure, wall pressure distribution, and unsteady aerodynamics, is investigated by testing and numerical simulation. The LSS experiments for the TSTO vehicle were performed using a high-speed pneumatic ejection launch system in the JF-12 shock tunnel, and the method was developed using high-speed visualization and image processing techniques to capture the separating trajectory. The numerical simulations were carried out using the overset grid method and solving the Navier–Stokes equations coupled with the rigid body dynamics equations to obtain the laminar flows over the TSTO vehicle during LSS. The qualitative and quantitative comparison of the test and numerical results showed good agreement in terms of aerodynamic performance, flowfield pattern, wall pressure, and separation trajectory. They show that the small interstage gap of the LSS leads to weak type I and VI shock–shock interactions, with short-duration weak shock reflection at a higher AoA. Furthermore, no shock reflection or interstage gap is observed at lower AoA. Moreover, no stage recontact is observed, and the safety and feasibility of LSS for parallel-staged TSTO vehicles are demonstrated.

Analysis of the thermal insulation performance of turbine blade thermal barrier coatings considering inlet non-uniformity

The gases discharged from the new generation of lean-burn combustors usually have hot streaks (HS) and swirls. The thermal performance of rotor thermal barrier coatings (TBCs) exhibits significant non-constant behavior due to inlet non-uniformity and blade row interaction. To investigate the non-constant thermal insulation performance of the blade TBCs, non-constant numerical simulations were carried out for the first stage vane and blade of the High-pressure turbine of the GE-E3 engine. The normalized temperature results for the HS and the combination of HS and swirl cases were compared with the uniform inlet case to investigate the effect of inlet non-uniformity on the surface temperature and thermal insulation effect of the blade TBCs. The results show that a credible investigation of rotor TBCs should consider the unsteady blade row interaction. HS causes high-temperature hot spots on the surface of the TBCs and redistributes them with the change in the direction of the swirl. HS and swirl significantly reduce the turbine blade cooling effectiveness and thermal insulation effectiveness of TBCs. The lowest overall cooling performance of the blades was observed during the 1/4 T stator period. The added swirl reduces the insulation effectiveness's fluctuation value by reducing positive swirl (PSW) by 52.6 % and negative swirl (NSW) by 57.8 %. Therefore, applications and designs of TBCs should consider the effects of HS and swirl.

Numerical investigation of communicating turbulent boundary layers through porous media

The reduction of trailing edge noise can be achieved through the use of porous trailing edges. It has been found that the unsteady interaction between the suction and pressure side of the airfoil is of relevance for noise reduction. Therefore, this study aims at investigating such ow physics. The proposed numerical setup consists of two vertically stacked temporally developing channel ows (4 ˇ (2 + t) ˇ 4, where and t are the half-charnnel height and the porous medium thickness respectively). The ow eld is solved using the lattice Boltzmann method through PowerFLOW. The two channel ows communicate through a fully resolved porous medium. In this work, the porous medium is a 75% porous Schwarz' P triply periodic minimal surface. Results show span-wise coherent turbulent structures developing on both sides of the porous medium. This is consistent with previous work on turbulent channels over porous media which enable ow in the stream-wise direction. However, the communication between both turbulent boundary layers results in these span-wise structures to be out-of-phase on either side of the permeable material. This phenomenon occurs at a frequency range where the noise reduction of porous trailing edges is the highest when compared to previous studies. A shift in turbulent kinetic energy carrying scales, with more energy being present in larger scales, is also observed. It can be concluded that this would increase the likelihood of interference occurring in the various locations of hydrodynamic pressure uctuation scattering and as such increase the noise reduction of porous trailing edges.

A Numerical Test Rig for Turbomachinery Flows Based on Large Eddy Simulations With a High-Order Discontinuous Galerkin Scheme—Part I: Sliding Interfaces and Unsteady Row Interactions

Abstract In this first paper of a three-part series, we present the extension and validation of the high-order discontinuous Galerkin scheme in DLR’s CFD-solver trace for scale-resolving simulations of unsteady row interactions. The translational movement of rows in linear cascade experiments is represented in the numerical model by solving the equations in the relative frame of reference. To couple rows in different frames of reference, a sliding interface approach based on the mortar technique for non-conforming meshes has been developed. The verification of the approach is exemplified by three canonical test cases. First, the experimental order of convergence is verified for the isentropic vortex convection. Subsequently, the suitability of the sliding interface approach for scale-resolving simulations is tested on the Taylor–Green vortex flow and a turbulent cylinder flow. Finally, the LES solver is applied to the T106D cascade with upstream moving bars at an exit Reynolds number of 200,000 and exit Mach number of 0.4. The flow physics with and without bars is discussed in terms of the instantaneous flow field, and time- and phase-averaged quantities. The comparison with experimental data shows overall a good agreement, especially for the total pressure losses in the wake, but also reveals uncertainties related to the reproduction of an experiment in the numerical model.

Effect of Unsteady Fan-Intake Interaction on Short Intake Design

Abstract The next generation of ultrahigh bypass ratio civil aero-engines promises notable engine cycle benefits. However, these benefits can be significantly eroded by a possible increase in nacelle weight and drag due to the typical larger fan diameters. More compact nacelles, with shorter intakes, may be required to enable a net reduction in aero-engine fuel burn. The aim of this paper is to assess the influence of the design style of short intakes on the unsteady interaction under crosswind conditions between fan and intake, with a focus on the separation onset and characteristics of the boundary layer within the intake. Three intake designs were assessed, and a hierarchical computational fluid dynamics (CFD) approach was used to determine and quantify primary aerodynamic interactions between the fan and the intake design. Similar to previous findings for a specific intake configuration, both intake flow unsteadiness and the unsteady upstream perturbations from the fan have a detrimental effect on the separation onset for the range of intake designs. The separation of the boundary layer within the intake was shock driven for the three different design styles. The simulations also quantified the unsteady intake flows with an emphasis on the spectral characteristics and engine-order signatures of the flow distortion. Overall, this work showed that is beneficial for the intake boundary layer to delay the diffusion closer to the fan and reduce the preshock Mach number to mitigate the adverse unsteady interaction between the fan and the shock.

Preliminary assessment of the NACA0021 trailing edge wedge for wind turbine application

The airfoil blade is the primary component of a wind turbine, and its aerodynamic properties play a crucial role in determining the energy conversion efficiency of these blades. Many researchers have proposed different airfoil modifications intending to enhance the aerodynamic characteristics and limit the unsteady interaction with the atmospheric boundary layer. This study evaluates the benefits of mounting wedge tails (WTs) on the trailing edge of an airfoil. The aerodynamic characteristics of a 2-D, steady-state NACA 0021 airfoil featuring the wedge tails (WT) and fish wedge tails (FWT) were studied computationally by employing the shear stress transport (SST) k-ω turbulence model. Different WT and FWT configurations were studied at various wedge length (L) to wedge height (H) ratios, L/H, at the airfoil's trailing edge. The effects of different L/H ratios, including L/H > 1, L/H = 1, and L/H < 1, were considered in the present study to determine the optimal configuration to achieve the maximum glide ratio, CL/CD at the Reynolds number of 180,000. The findings indicate that the performance of the NACA 0021 airfoil was notably affected by the height of the tail; however, the length had only a minor impact when L/H was less than 1. The mounted FWT resulted in significant enhancements to both the lift and glide ratio of the airfoil. Specifically, the lift ratio experienced an increase of over 41 % compared to the clean airfoil, while the glide ratio increased by more than 31 %. These improvements were observed at an ideal height and length of 2.5 % and 1 % of the airfoil, respectively. Moreover, the mounted FWT performed better than the Gurney flap using the same configurations.

Correlation of wall heat loss with quenching distance for premixed H2/Air flames during unsteady Flame-Wall interaction

Flame-wall interaction (FWI) of a laminar, premixed hydrogen/air flame perturbed by a pulsating inflow with excitation frequency (f) is investigated using fully resolved simulations employing finite-rate chemistry and detailed molecular diffusion. The setup is a two-dimensional (2D) V-shaped flame interacting with an isothermal wall on one side and a freely propagating flame on the other side, exhibiting a side-wall quenching and a freely-propagating mode. The impact of unsteady flame stretch on flame dynamics is characterized by the Damköhler number (Da), which is defined by the ratio of the turnover time of the oscillating inflow to the flame transit time. Da is found to directly describe the degree of flame deformation during flame propagation. During FWI, flame pocket formation is suppressed at conditions with Da close to unity. The correlation between wall heat flux (WHF) and quenching Peclet number (Peq) shows a time delay that depends on Da. A negative linear correlation can be recovered between time-averaged wall heat flux (WHF¯) with the quenching Peclet number (Peq¯), and its slope depends on the fuel equivalence ratio. For the lean hydrogen flame, the flame stretch near the quenching point leads to a decrease in flame intensity during FWI and therefore different slope of the correlation of WHF vs. Peq.

On the unsteady interactions between a sweeping jet and afterbody vortices

In this paper, a sweeping jet was applied to control the afterbody vortices behind a 30° slanted-base cylinder at a Reynolds number of 87 000. Phase-locked stereo particle image velocimetry measurements were conducted during a sweeping jet actuation cycle, and insights of the complex three-dimensional interaction process between the sweeping jet and the afterbody vortices have been obtained for the first time. It is found that in the near-field of the jet orifice (x/c &amp;lt; 0.3), the jet swings from side to side over the endplate between the afterbody vortex pair. An intersection between them around x/c = 0.3 causes the sweeping jet to take on a zigzag pattern as it propagates downstream along the slanted surface. From x/c = 0.6 onwards, the intensity of this interaction decreases as the afterbody vortices become detached from the base. Nevertheless, the sweeping jet continues invading the afterbody vortices from their inner side and pushes its way outwards from the underside of the afterbody vortices causing them to weaken further. Furthermore, the interaction between sweeping jets and afterbody vortices results in a cyclic variation in the circulation of afterbody vortices, which increases in magnitude at downstream locations. Except for the phases where a merger between the afterbody vortex and the sweeping occurs, a reduction in the circulation is observed. Finally, the level of interaction between sweeping jets and afterbody vortices intensifies as the strength of the sweeping jet increases resulting in the afterbody vortices being penetrated by the sweeping jet and their regular shape being momentarily destroyed.

Investigation of Vaned-Recessed Casing Treatment in a Low-Speed Axial-Flow Compressor, Part II: Unsteady Results

In this paper, unsteady characteristics of a modified vaned-recessed casing treatment with 23.2% rotor blade tip axial chord exposure were studied numerically. The modifications to the traditional vaned-recessed casing treatments were composed of geometrical amendments to the casing treatment’s guide vanes and the top of the treated casing. The solid casing and the casing treatment configurations were simulated using the Unsteady Reynolds-Averaged Navier–Stokes equations (URANS), and the results were validated by experimental results. Firstly, standard deviation and frequency analysis were performed to find the sources of unsteadiness. Secondly, velocity components analysis, including velocity triangles, was presented instantaneously to clarify their effects on rotor tip flow fields as well as stall margin improvement. Thirdly, unsteady interactions between the rotor and casing treatment flow fields, including flow structure and pressure distributions, were discussed. In the end, flow streamline patterns, in addition to the physical mechanism of the vaned-recessed casing treatment, were also discussed. The results indicated that unsteadiness plays an important role in the flow mechanism and cannot be ignored. The unsteadiness increases as the mass flow is reduced toward the stall/surge condition. Moreover, the analysis of velocity components demonstrated that the casing treatment has distinct behavior at the last operating points before the onset of the stall for solid casing and casing treatment configurations in terms of axial velocity change.

The Aerodynamic Performance of Horizontal Axis Wind Turbines under Rotation Condition

The near-surface unsteady incoming flow in the atmospheric boundary layer has a great influence on the aerodynamic performance of horizontal axis wind turbines. To consider the effect of the rotation of the blade on the aerodynamic state of a wind turbine near the ground, the fluid-structure interaction (FSI) method based on the shear stress transfer (SST) turbulence model is applied to analyze the unsteady aerodynamic interaction characteristics including solving the velocity field, pressure field, structural response state, variation of deformation, and output power in the flow field of the wind turbine. The deformation fluctuation points of different blades in the upwind and downwind regions were observed to move towards the blade tips with increasing rotational speed. The variations of flow velocity and pressure that occur along the radial direction of the wind turbine are observed. The velocity increases from the root to the tip of the blade. The tower shadow effect causes the blade deformation in the upper and lower wind areas to fluctuate. It is more obvious when the blade overlaps with the tower; the overall displacement under the effect of rotation has a large increase compared with the shutdown. The peak increments reach 2.1437 mm to 0.8674 mm; under the effect of inter-action wind speed increased, wind turbine output power increased from 68.33 kW to 84.33 kW, respectively. It helps to better understand the aerodynamic performance of wind turbines, prolong the service life, and optimize the design.

Numerical Investigation of Rotating Instability Development in a Wide Tip Gap Centrifugal Compressor

In the current study, full-stage unsteady simulations were performed to investigate rotating instability inception mechanisms in a particularly large tip clearance centrifugal compressor with a vaneless diffuser and a volute. Four operating points along a speed line were analysed to understand the influence of the mass flow reduction on flow structures. Close to the peak efficiency, an unsteady interaction between the tip clearance vortices and splitter blades was observed. Considering other studies, the influence of the tip gap size was analysed. Then, a large-scale vortex shedding from the leading edges of the main blades was detected when the stage operated near the maximum pressure ratio. It was demonstrated that shed vortices were caused by the combination of the radial gradient of the tangential velocity under the tip vortex and the reverse backflow near the casing. Previous studies on axial compressors refer to these vortical structures as backflow vortices. These vortices cause a significant increase in the incidence angle in the tip region.

Unsteady Aeroelastic Characterization and Scaling Relations of Flexible Membrane Wings

We present a numerical study to characterize nonlinear unsteady aeroelastic interactions of two-dimensional flexible wings at high angles of attack. The coupled fluid–flexible wing system is solved by a body-fitted variational aeroelastic solver based on the fully coupled Navier–Stokes and nonlinear structural equations. Using the coupled fluid–structure analysis, this study is aimed to provide physical insight and correlations for the aeroelastic behavior of flexible wings in the parameter space of the angle of attack and the aeroelastic number. The phase diagrams of the aerodynamic performance are established to obtain the envelope curves of the optimal performance and determine the transition line of the drag variation. The effects of the angle of attack and the aeroelastic number on the aeroelastic behaviors are systematically examined. The time-averaged membrane deformation is positively correlated with a nondimensional number, the so-called Weber number. A new scaling relation is proposed based on the dynamic equilibrium between the aerodynamic force fluctuation and the combined inertia–elastic fluctuation. The unsteady aerodynamic force can be adjusted by manipulating the membrane vibration, the mass ratio, the Strouhal number, and the aeroelastic number. The numerical investigations provide design guidelines and have the potential to enhance the maneuverability and flight agility of micro air vehicles with flexible wing structures.

Study on gasdynamic interaction in a regulated two-stage turbocharging turbines at pulsating conditions

Understanding the response of performance of two-stage turbine to pulsating flow in exhaust manifold system is essential for performance improvement of engine. This paper studies unsteady interaction of two turbines in a two-stage turbocharging system via experimental method and a reduced order model. Firstly, experimental results of the unsteady pressure ratio of two turbines are discussed in cases with different engine speeds, engine loads, and bypass valve openings. Results show that the pressure ratio distribution between two turbines is profoundly influenced by the engine condition. The pressure ratio of low-pressure turbine (LPT) increases consistently with the engine speed and load, while it increases slightly or even remains unchanged for high-pressure turbine (HPT). HPT is de-loaded when the bypass valve is open, and there are large numbers of fluctuations with high frequencies in the trace of pressure ratio when the bypass valve is open. Next, a reduced order model of the two-stage turbine is established for turbine responses at pulsating conditions, and model validations of performance and unsteady pressure in two-stage turbine all show high precision. Finally, the model is applied for performance analysis of two-stage turbine system under pulsating conditions. The results show that with the increase in engine speed, load or bypass valve opening, the hysteresis loops of both turbines are expanded around the steady performance curve. However, the deviation of cycle-average performance from steady case for two turbines is notably different. LPT shows a stronger throttling effect at pulsating inflows. Moreover, compared with steady performance for whole two-stage turbine, cycle-average performance is reduced for all pulsating cases, especially for cases of open valve. The differences in turbine performance of two-stage turbine system caused by gasdynamic coupling effect of two turbines are suggested to be considered in the turbo-engine matching.

High-fidelity simulations of the aeroacoustic environment of the VEGA launch vehicle at lift-off

The lift-off of space launch vehicles generates strong acoustic waves that interact in a complex and potentially dangerous way with the launch facility and the launcher itself. Engineering tools developed in the past to predict the strong acoustic radiation and the peak acoustic loads during the first seconds of the launch have a limited validity and are not able to provide reliable predictions. For this reason, in order to better identify the noise generation sources and to assess the effects of acoustic mitigation measures, it is fundamental to develop and validate more advanced computational models able to capture the transient flow induced by the ignition of the motors. In this work, we present high-fidelity 3D Large Eddy Simulations of the acoustic field produced by the lift-off of a realistic space launcher. A state-of-the-art, high-order, GPU accelerated, compressible solver is used to simulate the highly unsteady interaction of the exhaust plume from the launcher’s nozzle with a realistic launch pad, whose geometry has been modelled by Immersed Boundary Method. The results obtained demonstrate the capability of our solver to provide accurate predictions compared to flight measurements of real configurations, despite the challenging scenario in terms of operating conditions and geometry. Moreover, wavelet analysis proves to be an appropriate tool to pinpoint and characterise the overpressure mechanisms that take place in the transient evolution of the flow.

Harmonic Method for Simulating Unsteady Multispool Interactions

Abstract Modern civil jet engines arrange components on spools with different rotational speeds in order to improve compressor stall margin, overall engine performance, etc. The unsteady interactions among these components can be significant and should be considered at an early design stage if possible. Unsteady Reynolds-averaged Navier–Stokes (URANS) is a common approach to simulate these unsteady effects, but the disparity in time scales in a multispool simulation can lead to expensive URANS simulations. Harmonic methods are effective and efficient approaches to simulate unsteady interactions among turbomachinery components, but their applications to multispool simulations remain a challenge. The objective of this paper is to address this challenge. This paper extends the Favre-averaged non-linear harmonic method to simulate multispool turbomachinery components using a unified bladerow interface which transfers disturbances through bladerows with arbitrary blade counts at any rotational speed. The regularization of non-reflective boundary condition is described for certain circumferential wave number of the zero-frequency mode. The capability of the proposed approach is demonstrated by simulating the transfer of hot streaks through full 3D high- and intermediate-pressure turbines in a three-shaft engine. The temperature distributions from the harmonic method show good agreement with direct unsteady simulation in terms of the mean flow and the instantaneous flow. The radial migration of the hot streaks towards the hub are captured very well by the proposed harmonic method. The required wall-clock time of the harmonic method is roughly 240 times smaller than the whole annulus URANS simulation. This demonstrates that the proposed method can be an efficient design tool to trace hot streaks in multispool turbines at the early design stage.

Compressible pairwise interaction extended point-particle model for force prediction of shock-particle bed interaction

Euler-Lagrange simulations are often required to study complex compressible multiphase problems. Such systems include volcanic explosions and supernovas. We developed an unsteady neighboring particle interaction framework with the help of the compressible Maxey-Riley-Gatignol equation and the scattering theory, which further improves force predictions used in Euler-Lagrange simulations.

Effects of inertia on the time-averaged propulsive performance of a pitching and heaving foil

The inertia may play an important role in the unsteady behavior of a flapping foil. Of particular relevance in forward flapping locomotion is how the foil inertia may affect its time-averaged propulsive performance. This is the question addressed by the present study from a general, nonlinear formulation of the unsteady interaction with the surrounding fluid of a thin, flexible, two-dimensional and non-uniform foil undergoing prescribed pitching and heaving motion of any amplitude about an arbitrary pivot axis. For a rigid foil it is shown that, although the unsteady inertial forces and moments may be much larger than the unsteady aerodynamic forces and moments if the fluid density is much smaller than the foil density, the inertia does not affect the cycle-averaged propulsive performance for harmonic pitching and heaving motion, independently of their amplitude. Inertia may affect only the cycle-averaged moment if the mean angle of attack is not zero, but without affecting the cycle-averaged power input, and therefore the propulsive efficiency. When a small flexural deflection of the foil is considered, although the cycle-averaged inertial thrust and lift also vanish for any amplitude of the pitching and heaving harmonic motion, the cycle-averaged power input does not. Thus, the foil inertia contributes through the moment and power to the time-averaged propulsive performance for any flexural deflection of the foil, obtained her e analytically in terms of the trailing edge location for general pitching and heaving motion of any amplitude and phase and small flexural deflection amplitude. Simple analytical results are also provided for inertia dominated deflection, characterizing the conditions that minimize the power consumption. The results are valid for arbitrary chord-wise distribution of mass, thickness and (sufficiently large) stiffness of the foil.

Effect of the radial gap size on the deterministic flow in a centrifugal pump due to impeller-tongue interactions

The research on the flow in centrifugal pumps is quite broad and covers most of the relevant issues. However, most of the studies are focused on the steady behaviors and less literature is available for the dynamic interactions. Unsteady mechanisms for energy transfer and sources of impeller-tongue interaction can be identified in centrifugal pumps using the deterministic decomposition of the flow. Probably, the most important effect to be considered is the radial gap or spacing between the impeller exit diameter and the volute tongue radial location. The numerical dataset of a full 3D URANS model in a centrifugal pump has been employed to study in detail the effect of the radial gap size in the unsteady fluctuations of the velocity field within the pump, using the deterministic analysis as the main novelty. The numerical model developed by the authors has been already tested towards the prediction of the unsteady pressure field inside the volute, at the impeller exit. The new results presented here allow to see the impact of both geometrical and operating parameters on the flow discharge and momentum exchange. In particular, four different radial gaps (23.2%, 17.0%, 11.4% and 8.8% of the impeller diameter) operated at five different flow rates (from 20% to 160% of the nominal rate) have been numerically resolved and analyzed. The deterministic analysis reveals the major impact of the radial clearance on the blade-to-blade flow patterns within the impeller, especially at low flow rates. Unsteady viscous interaction induces radial velocity fluctuations that can be as high as a 40% of the time-averaged value. Moreover, this non-linear term can be perceived up to 1.5 times higher in the case of radial gap reductions from 23.2% to 8.8% of the impeller diameter. There is not a prevailing effect of the radial gap on that velocity component, and a pure temporal term dependence is found. On the contrary, the influence of the gap on the tangential component, responsible for the unsteady evolution of the impeller torque, is found to be the key parameter. Therefore, the fluctuations of the flow blockage are found to be the consequence of the impeller flow patterns and the fluctuations of the torque are to be assigned to the radial gap influence. All the post-processing routines have provided a precise picture of all the classic unsteady mechanisms involved: jet-wake pattern interaction, acoustic wave propagations and recirculating cells at off-design conditions. Hence, deterministic analysis is a useful tool to analyze the flow inside centrifugal pumps and it envisages the introduction of deterministic flow variables as objective functions for design optimization algorithms.