Time-accurate Computational Fluid Dynamics Research Articles

An in-silico analysis of hydrodynamics and gas mass transfer characteristics in scale-down models for mammalian cell cultures

Bioprocess scale-up and technology transfer can be challenging due to multiple variables that need to be optimized during process development from laboratory scale to commercial manufacturing. Cell cultures are highly sensitive to key factors during process transfer across scales, including geometric variability in bioreactors, shear stress from impeller and sparging activity, and nutrient gradients that occur due to increasing blend times. To improve the scale-up and scale-down of these processes, it is important to fully characterize bioreactors to better understand the differences that will occur within the culture environment, especially the hydrodynamic profiles that will vary in vessel designs across scales. In this study, a comprehensive hydrodynamic characterization of the Ambr® 250 mammalian single-use bioreactor was performed using time-accurate computational fluid dynamics simulations conducted with M-Star computational fluid dynamics software, which employs lattice-Boltzmann techniques to solve the Navier-Stokes transport equations at a mesoscopic scale. The single-phase and two-phase fluid properties within this small-scale vessel were analyzed in the context of agitation hydrodynamics and mass transfer (both within the bulk fluid and the free surface) to effectively characterize and understand the differences that scale-down models possess when compared to their large-scale counterparts. The model results validate the use of computational fluid dynamics as an in-silico tool to characterize bioreactor hydrodynamics and additionally identify important free-surface transfer mechanics that need to be considered during the qualification of a scale-down model in the development of mammalian bioprocesses.

Computational and Experimental Study of the Unsteady Convection of Entropy Waves Within a High-Pressure Turbine Stage

Abstract This article describes the transport and the interaction of pulsating entropy waves generated by combustor burners within a high-pressure turbine stage for aeronautical application. Experiments and computational fluid dynamics (CFD) simulations were carried out in the context of the European Research Project RECORD. Experimental campaigns considering burner-representative temperature fluctuations (in terms of spot shape, fluctuation frequency, and total temperature variation percentage) injected upstream of an un-cooled high-pressure gas turbine stage have been performed in the high-speed closed-loop test rig of the Fluid Machine Laboratory (LFM) of the Politecnico di Milano (Italy). The pulsating entropy waves are injected at the stage inlet in streamwise direction at four different azimuthal positions featuring a 7% overtemperature with respect to the main flow with a frequency of 90 Hz. Detailed time-resolved temperature measurements (in the range of 0–200 Hz) upstream and downstream of the stage, as well as in the stator–rotor axial gap, were performed. Time-accurate CFD simulations with and without entropy fluctuations imposed at the stage inlet were performed with the TRAF code, developed by the Università degli Studi di Firenze (Italy). A numerical postprocessing procedure, based on the discrete Fourier transform (DFT) of the conservative variables, has been implemented to extract the low-frequency content connected to the entropy fluctuations. Measurements highlighted a significant attenuation of the entropy wave spot throughout their transport within the stator channel and their interaction with the rotor blade rows, highly depending on their injection azimuthal position. Simulations show an overall good agreement with the experiments on the measurement traverses, especially at the stage outlet. By exploiting the combination of experiments and simulations, the aerodynamic and thermal implications of the temperature fluctuation injected upstream of the stage were properly assessed, thus allowing suggest useful information to the designer. The comparison with the experiments confirms the accuracy of the CFD method to solve the periodic, but characterized by a low-frequency content event, associated with the entropy wave fluctuation.

Direct Comparison of Immersion and Cold-Plate Based Cooling for Automotive Li-Ion Battery Modules

The current paper evaluates the thermal performance of immersion cooling for an Electric Vehicle (EV) battery module comprised of NCA-chemistry based cylindrical 21700 format Lithium-ion cells. Efficacy of immersion cooling in improving maximum cell temperature, cell’s temperature gradient, cell-to-cell temperature differential, and pressure drop in the module are investigated by direct comparison with a cold-plate-cooled battery module. Parametric analyses are performed at different module discharge C-rates and coolant flow rates to understand the sensitivity of each cooling strategy to important system performance parameters. The entire numerical analysis is performed using a validated 3D time-accurate Computational Fluid Dynamics (CFD) methodology in STAR-CCM+. Results demonstrate that immersion cooling due its higher thermal conductance leads to a lower maximum cell temperature and lower temperature gradients within the cells at high discharge rates. However, a higher rate of heat rejection and poor thermal properties of the dielectric liquid results in a much higher temperature non-uniformity across the module. At lower discharge rates, the two cooling methods show similar thermal performance. Additionally, owing to the lower viscosity and density of the considered dielectric liquid, an immersion-cooled battery module performs significantly better than the cold-plate-cooled module in terms of both coolant pressure drop.

Calcia–magnesia–alumina-silica particle deposition prediction in gas turbines using a Eulerian–Lagrangian approach in computational fluid dynamics

Abstract

Computational and Experimental Study of Hot Streak Transport Within the First Stage of a Gas Turbine

Abstract The paper discusses the migration, the interaction with the blades, and the attenuation of hot streaks generated by combustor burners, during their propagation within the first turbine stage of aero-engines. Experiments and computational fluid dynamics (CFD) simulations were carried out in the framework of the European Project RECORD and on its follow-up. Measurements considering burner-representative temperature perturbations injected upstream of an un-cooled high-pressure gas turbine stage were performed in the high-speed closed-loop test-rig of the Politecnico di Milano (Italy). The hot streaks were injected in a streamwise direction at the stage inlet in four different circumferential positions with respect to the stator blade. They feature a 20% over-temperature with respect to the main flow. Detailed temperature measurements as well as unsteady aerodynamic measurements upstream and downstream of the blade rows were performed. Time-accurate CFD simulations of the flow upstream and within the turbine stage were performed with the TRAF code, developed by the Università degli Studi di Firenze (Italy). Measurements show a relevant attenuation of hot streaks throughout their transport within the stator and the rotor blade rows, highly depending on the injection azimuthal position. The perturbations were observed to lose their spatial coherence, especially in the transport within the rotor, and to undergo severe spanwise migration. Simulations exhibit a good agreement with the experiments on the measurement planes and allow tracking the complex flow phenomena occurring within the blade rows. Finally, the aerodynamic and thermal implications of the inlet temperature perturbations are properly highlighted and discussed.

이동변형격자 기법을 활용한 외부장착물 분리운동 해석

A military aircraft generally includes external stores such as fuel tanks or external arming, depending on the purpose of the operation. When a store is dropped from a military aircraft at high subsonic, transonic, or supersonic speeds, the aerodynamic forces and moments acting on the store can be sufficient to send the store back into contact with the aircraft. This can cause damage to the aircraft and endanger the life of the crew. In this study, time accurate computational fluid dynamics (CFD) with dynamic moving grid (moving and deformable mesh, MDM) technique has been used to accurately calculate store trajectories. For the verification of the present numerical approach, a wind tunnel test model for the wing-pylon-finned store configuration has been considered and analyzed. The comparison results for the ejected store trajectories between the present numerical analysis and the wind tunnel test data at the Mach number of 0.95 and 1.2 are presented. It is also importantly shown that the numerical parameter of MDM technique gives significant effect for the calculated store trajectory in the low-supersonic flow such as Mach 1.2.

Efficient Fluid-Thermal-Structural Time Marching with Computational Fluid Dynamics

This study focuses on the development of time-marching procedures for efficient and accurate fluid-thermal-structural analysis with time-accurate computational fluid dynamics. The developed procedures are based on a loosely coupled, partitioned framework for the fluid, thermal, and structural solvers—each with different second-order time integrators. The procedures also implement subcycling, where disparate time scales between the solvers are leveraged to minimize communication between solvers. The first scheme uses a second-order predictor of fluid loads, along with second-order interpolations of structural and thermal solutions. The second scheme is an extension that adds a corrector step to the structural and thermal solvers. The two schemes are benchmarked against both a strongly coupled approach with subiterations and a basic loosely coupled approach that omits the use of predictors/correctors. The schemes are examined in the context of the aerothermoelastic response of a panel in high supersonic flow, and are found to maintain second-order time accuracy with and without subcycling. Furthermore the approaches compare favorably against a strongly coupled approach at significantly reduced computational times, with the predictor-corrector approach yielding speedups of 2–4 times. In comparison, a basic scheme can yield characteristically different behavior.

Rapid Transonic Flutter Analysis for Aircraft Conceptual Design Applications

This study presents a new approach for the rapid transonic flutter analysis of large-aspect-ratio wings via a combination of time-linearized two-dimensional unsteady indicial functions and a database of steady two-dimensional Reynolds-averaged Navier–Stokes simulations. The approach is limited to large-aspect-ratio wings that can be discretized into multiple, streamwise, independent strips; and the well-documented “strip theory” with sweep corrections is applicable. This formulation allows the extension of Leishman’s indicial functions (“Validation of Approximate Indicial Aerodynamic Functions for Two-Dimensional Subsonic Flow,” Journal of Aircraft, Vol. 25, No. 10, 1988, pp. 914–922) to three-dimensional wings but also restricts the present method to attached flows. However, when supported with two-dimensional steady Reynolds-averaged Navier–Stokes simulations, the present method predicts flutter speeds that are within 10% of that predicted by two-dimensional time-accurate Reynolds-averaged Navier–Stokes simulations. Application of the proposed method for a large-aspect-ratio wing is validated by comparing the predicted flutter boundary against wind-tunnel experiments. More importantly, the current method predicts the transonic dip phenomena observed in the experiments but not predicted by NASTRAN analysis. This is achieved at several orders-of-magnitude lower computation time than high-fidelity time-accurate computational fluid dynamics simulations. The level of accuracy obtained at such an extremely low computation time makes the present approach very suitable for applications in conceptual design studies of large-aspect-ratio transonic vehicles.

Numerical Simulation of Dynamic Stall Characteristics for Wind Turbine under Yawed Condition

When a horizontal axis wind turbine rotor works under yawed condition, a cyclic variation of Angle of Attack (AOA) at blades will causes dynamic stall phenomenon and accordingly increases the fatigue load. In order to relate the yawed condition with dynamic stall characteristic, a 3D and time-accurate Computational Fluid Dynamics (CFD) is used for the simulations of flow-field and dynamic stall characteristic on the National Renewable Energy Laboratory (NREL) Phase VI wind turbine rotor at yaw 30 degrees. The local AOA and airfoil aerodynamics, i.e., lift coefficient Cl and drag coefficient Cd, are computed based on CFD results. The results show that the horizontal component of yawed inflow and unsteady flow around sections of blade will delay the formation of separation vortex and also the occurrence of stall. The dynamic load accompanied with dynamic stall phenomenon is significantly increased on blade, and the hysteresis characteristic of airfoil lift and drag is more remarkable at the inboard blade sections. The derived results are helpful to develop more reliable aerodynamic models for wind turbine design codes, and also can provide theoretical guidance for the optimal design of a wind turbine.

Hover Predictions on the S-76 Rotor with Tip Shape Variation Using Helios

High-resolution, time-accurate computational fluid dynamics validation of a 9.34 ft, four-blade, Mach-scaled S-76 rotor in hover is performed using the U.S. Department of Defense Computational Research and Engineering Acquisition Tools and Environments–Air Vehicles Helios software. The effect of blade tip shape variation is studied for three tip shapes: rectangular, swept tapered, and swept tapered anhedral. The effect of tip Mach number is studied for the swept-tapered tip. Computed results include rotor performance, blade airloads, and tip-vortex strength and position. The performance predictions are compared against the test measurements and good agreement is obtained. Compared with the swept-tapered tip, the rectangular blade incurs compressibility losses near the tip. The addition of anhedral to the swept-tapered tip improves performance as a result of redistribution of thrust.

In Situ Distribution Guided Analysis and Visualization of Transonic Jet Engine Simulations.

Study of flow instability in turbine engine compressors is crucial to understand the inception and evolution of engine stall. Aerodynamics experts have been working on detecting the early signs of stall in order to devise novel stall suppression technologies. A state-of-the-art Navier-Stokes based, time-accurate computational fluid dynamics simulator, TURBO, has been developed in NASA to enhance the understanding of flow phenomena undergoing rotating stall. Despite the proven high modeling accuracy of TURBO, the excessive simulation data prohibits post-hoc analysis in both storage and I/O time. To address these issues and allow the expert to perform scalable stall analysis, we have designed an in situ distribution guided stall analysis technique. Our method summarizes statistics of important properties of the simulation data in situ using a probabilistic data modeling scheme. This data summarization enables statistical anomaly detection for flow instability in post analysis, which reveals the spatiotemporal trends of rotating stall for the expert to conceive new hypotheses. Furthermore, the verification of the hypotheses and exploratory visualization using the summarized data are realized using probabilistic visualization techniques such as uncertain isocontouring. Positive feedback from the domain scientist has indicated the efficacy of our system in exploratory stall analysis.

A Three-Dimensional Time-Accurate Computational Fluid Dynamics Simulation of the Flow Field Inside a Vaneless Diffuser During Rotating Stall Conditions

An accurate characterization of rotating stall in terms of inception modality, flow structures, and stabilizing force is one of the key goals for high-pressure centrifugal compressors. The unbalanced pressure field that is generated within the diffuser can be in fact connected to a non-negligible aerodynamic force and then to the onset of detrimental subsynchronous vibrations, which can prevent the machine from operating beyond this limit. An inner comprehension on how the induced flow pattern in these conditions affects the performance of the impeller and its mechanical stability can therefore lead to the development of a more effective regulation system able to mitigate the effects of the phenomenon and extend the left-side margin of the operating curve. In the present study, a 3D-unsteady computational fluid dynamics (CFD) approach was applied to the simulation of a radial stage model including the impeller, the vaneless diffuser, and the return channel. Simulations were carried out with the TRAF code of the University of Florence. The tested rotor was an industrial impeller operating at high peripheral Mach number, for which unique experimental pressure measurements, including the spatial reconstruction of the pressure field at the diffuser inlet, were available. The comparison between experiments and simulations showed a good matching and corroborated the CFD capabilities in correctly describing also some of the complex unsteady phenomena taking place in proximity of the left margin of the operating curve.

An easy-to-use turbulent inlet boundary condition for large-eddy simulation of radial diffusers

When applying time-accurate computational fluid dynamics, large-eddy simulation (CFD LES) to room ventilation, a common problem is that the supply jets do not model properly if there is no realistic turbulence in the inflow boundary. In this paper we introduce a novel, easy-to-use method of generating a turbulent inlet boundary condition for simulating a radial diffuser. The basic idea is to apply a time-independent velocity distribution with realistic spatial statistics, and to add temporal fluctuations by rotation. The method is simple to use, requires only one extra parameter, and does not necessitate large storage files. It needs a momentary velocity distribution on the inflow surface with the desired volume flow rate obtained from a time-accurate internal simulation of the diffuser alone. In a room-scale simulation, this velocity distribution is put in rotating movement in order to mimic a turbulent inlet boundary. The method is verified by comparing the outcome with published measurements and with a simulation containing the interior of the diffuser.

Analysis and Prediction of Shock-Induced Vortex Circulation in Transonic Compressors

Multiple high-fidelity time-accurate computational fluid dynamics simulations were performed to investigate the effects of upstream stator loading and rotor shock strength on vortex shedding characteristics in a single-stage transonic compressor. Three loadings on the upstream stator row of decreased, nominal, and increased loading in conjunction with three axial spacings of close, mid, and far were studied for this analysis. The time-accurate urans code turbo was used to generate periodic, quarter annulus simulations of the blade row interaction (BRI) compressor rig. It was observed that vortex shedding was synchronized to the passing of a rotor bow shock. Results show that vortex strength increases linearly with stator loading and rotor bow shock strength. “Normal” and “large” shock-induced vortices formed on the stator trailing edge (TE) immediately after the shock passing, but the large vortices were strengthened at the TE due to a low-velocity region on the suction surface. This low-velocity region was generated upstream on the suction surface from a shock-induced thickening of the boundary layer or separation bubble. The circulation of the large vortices was greater than the normal vortices by a factor of 1.7, 1.83, and 2.04 for decreased, nominal, and increased deswirler loadings. At decreased loading, only 24% of the measured vortices were considered large, while at nominal loading 58% were large. A model was developed to predict shock-induced vortex circulation from a known rotor bow shock strength, stator diffusion factor, and near-wake parameters. The model predicts the average vortex circulation very well, with 5% difference between predicted and measured values. An understanding of the unsteady interactions associated with blade loading and rotor shock strength in transonic stages will help compressor designers account for unsteady flow physics at design and off-design operating conditions.

Determining Sources of Unsteady Energy Transfer in Time-Accurate Computational Fluid Dynamics

With the increase in computational resources, time-accurate reacting flow, computational fluid dynamics have improved to the point where periodic, unsteady behavior associated with hydrodynamic instability and acoustic resonance can be accurately modeled. However, computational fluid dynamics solutions, like experiments, only reveal the manifestation of unstable behavior such as pressure fluctuations or vortex generation. They do not readily divulge the sources of energy transfer leading to and sustaining instabilities. Because of this, it can be arduous to correlate design decisions with overall system stability using computational fluid dynamics alone. Combining the well-established unsteady energy transport theory and a choice of viable data analysis techniques, a rigorous approach for analyzing time-accurate computational fluid dynamics solutions is established. Through this approach, the sources of driving and damping can be visualized and quantified. Thereby, the aforementioned issue is rectified and a deeper insight into the root causes of instability and its overall effect is achieved.

Reduced-order modelling of wind turbine airfoil unsteady aerodynamic loading

In this paper, three different reduced-order models (auto-regressive and moving average, Volterra series and a surrogate-based recurrence framework model) are presented for the prediction of the unsteady dynamic loading of wind turbine airfoils. A wind turbine blade section can experience unsteady aerodynamic loads when subjected to an unsteady aerodynamic environment. The generations of three reduced-order models for the evaluation of unsteady aerodynamic loads are investigated, with the different models used as a representation of linear or non-linear loading. The validity of the presented reduced-order models is assessed mainly by comparing the model output with unsteady time-accurate computational fluid dynamics (CFD) simulations. The results reveal an encouraging agreement between the computational fluid dynamics simulations and the model predictions under different conditions. All three reduced-order models would therefore be useful in engineering conditioning for aeroelastic analysis and wind turbine design optimization.

Time-Resolved Heat Transfer and Surface Pressure Measurements for a Fully Cooled Transonic Turbine Stage

The flow field in axial gas turbines is driven by strong unsteady interactions between stationary and moving components. While time-averaged measurements can highlight many important flow features, developing a deeper understanding of the complicated flows present in high-speed turbomachinery requires time-accurate measurements that capture this unsteady behavior. Toward this end, time-accurate measurements are presented for a fully cooled transonic high-pressure turbine stage operating at design-corrected conditions. The turbine is run in a short-duration blowdown facility with uniform, radial, and hot streak vane-inlet temperature profiles as well as various amounts of cooling flow. High-frequency response surface pressure and heat-flux instrumentation installed in the rotating blade row, stator vane row, and stationary outer shroud provide detailed measurements of the flow behavior for this stage. Previous papers have reported the time-averaged results from this experiment, but this paper focuses on the strong unsteady phenomena that are observed. Heat-flux measurements from double-sided heat-flux gauges (HFGs) cover three spanwise locations on the blade pressure and suction surfaces. In addition, there are two instrumented blades with the cooling holes blocked to isolate the effect of just blade cooling. The stage can be run with the vane and blade cooling flow either on or off. High-frequency pressure measurements provide a picture of the unsteady aerodynamics on the vane and blade airfoil surfaces, as well as inside the serpentine coolant supply passages of the blade. A time-accurate computational fluid dynamics (CFD) simulation is also run to predict the blade surface pressure and heat-flux, and comparisons between prediction and measurement are given. It is found that unsteady variations in heat-flux and pressure are stronger at low to midspan and weaker at high span, likely due to the impact of secondary flows such as the tip leakage flow. Away from the tip, it is seen that the unsteady fluctuations in pressure and heat-flux are mostly in phase with each other on the suction side, but there is some deviation on the pressure side. The flow field is ultimately shown to be highly three-dimensional, as the movement of high heat transfer regions can be traced in both the chord and spanwise directions. These measurements provide a unique picture of the unsteady flow physics of a rotating turbine, and efforts to better understand and model these time-varying flows have the potential to change the way we think about even the time-averaged flow characteristics.

Helicopter Rotor Design Using a Time-Spectral and Adjoint-Based Method

A time-spectral and adjoint-based optimization method was developed and applied to helicopter rotor design for unsteady level flight. The time-spectral method is a fast and accurate computational fluid dynamics algorithm for computing unsteady flows. It transforms the flow-governing equations into a periodic steady state by using a Fourier spectral derivative operator. An accompanying steady-state adjoint formulation was implemented in the time-spectral form of the governing equations to enable design optimization for unsteady flows. The time-spectral analysis was validated against conventional time-accurate computational fluid dynamics computation and flight test data of a UH-60A helicopter rotor during high-speed forward flight. A multidisciplinary analysis of blade structural dynamics was carried out through a comprehensive analysis coupling procedure that accounted for aeroelasticity and enforced vehicle trim. The adjoint-based design method was applied to optimize the blade shape of the UH-60A rotor. Power minimization was pursued with nonlinear constraints on the thrust and rotor drag force. The blade twist distribution, sectional airfoil shape, and outboard planform shape comprised over 100 design variables. Starting from the initial blade, the optimizer found a new design that showed improved performance. The validation results coupled with the multidisciplinary comprehensive analysis confirmed actual improvement: a 5% decrease in torque accompanied by a decrease in thrust of less than 1%.

A Locally Parametrized Reduced-Order Model for the Linear Frequency Domain Approach to Time-Accurate Computational Fluid Dynamics

For transonic flows governed by the time-accurate Navier--Stokes equations, small, approximately periodic perturbations can be calculated accurately by transition to the frequency domain and truncating the Fourier expansion after the first harmonic. This is referred to as the linear frequency domain (LFD) method. In this paper, a parametric trajectory of reduced-order models (ROMs) for the LFD solver is presented. To this end, several local projection-based ROMs, which are essentially specified by suitable low-order subspaces, are computed by the method of proper orthogonal decomposition (POD) in an offline stage. The claimed trajectory is obtained locally by interpolating the given local subspaces considered as sample points in the Grassmann manifold. It is shown that the manifold interpolation technique is subject to certain restrictions. Moreover, it turns out that the application of computing accurate ROMs for the LFD solver requires a special choice of underlying inner product, necessitating a non-Eu...

Time-accurate CFD conjugate analysis of transient measurements of the heat-transfer coefficient in a channel with pin fins

Heat-transfer coefficients (HTC) on surfaces exposed to convection environments are often measured by transient techniques such as thermochromic liquid crystal (TLC) or infrared thermography. In these techniques, the surface temperature is measured as a function of time, and that measurement is used with the exact solution for unsteady, zero-dimensional (0-D) or one-dimensional (1-D) heat conduction into a solid to calculate the local HTC. When using the 0-D or 1-D exact solutions, the transient techniques assume the HTC and the free-stream or bulk temperature characterizing the convection environment to be constants in addition to assuming the conduction into the solid to be 0-D or 1-D. In this study, computational fluid dynamics (CFD) conjugate analyses were performed to examine the errors that might be invoked by these assumptions for a problem, where the free-stream/bulk temperature and the heat-transfer coefficient vary appreciably along the surface and where conduction into the solid may not be 0-D or 1-D. The problem selected to assess these errors is flow and heat transfer in a channel lined with a staggered array of pin fins. This conjugate study uses three-dimensional (3-D) unsteady Reynolds-averaged Navier–Stokes (RANS) closed by the shear-stress transport (SST) turbulence model for the gas phase (wall functions not used) and the Fourier law for the solid phase. The errors in the transient techniques are assessed by comparing the HTC predicted by the time-accurate conjugate CFD with those predicted by the 0-D and 1-D exact solutions, where the surface temperatures needed by the exact solutions are taken from the time-accurate conjugate CFD solution. Results obtained show that the use of the 1-D exact solution for the semi-infinite wall to give reasonably accurate “transient” HTC (less than 5% relative error). Transient techniques that use the 0-D exact solution for the pin fins were found to produce large errors (up to 160% relative error) because the HTC varies appreciably about each pin fin. This study also showed that HTC measured by transient techniques could differ considerably from the HTC obtained under steady-state conditions with isothermal walls.