CFD Solutions Research Articles

An improved model for predicting dynamic total pressure distortion

In order to accurately predict the dynamic total pressure distortion produced by crescent baffle distortion simulator in its practical application, an improved turbulence correlation model is proposed in this paper. Several turbulence parameters from CFD solution are correlated with the measured turbulence via the improved model. Back-propagation artificial neural network (BP ANN) is used to find the correlation and establish a turbulence prediction model. Dynamic distortion intensity is represented by the predicted turbulence. The results show that dynamic distortion indexes predicted by the improved model are more accurate, with a maximum error of 7.72%. Finally, the dynamic distortion flow field of crescent baffle distortion simulator is predicted by applying the established prediction model. Analysis of dynamic distortion characteristics provides important guidance for the application of crescent baffle distortion simulator.

A CFD-adjoint reverse design of transverse rib profile for enhancing thermo-hydraulic performance in the solar air heater

Artificial ribs interrupting the viscous sublayer beneath the absorbing plate are used to enhance SAH heat efficiency. In the present study, the CFD-adjoint reverse design method is developed to intelligently design the rib profile. Based on the zero-order CFD solution, the shape sensitivity of the rib profile is calculated by the CFD-adjoint solver, which identifies the profile characteristics to improve thermo-hydraulic performance (THPP). According to the shape sensitivity, the reverse design is conducted with geometrical constraints, optimization algorithms, and mesh deformation. To maximize THPP, five novel ribs are reversely designed under Reynolds numbers ranging from 4000 to 16000. The flow and heat transfer characteristics of the reversely designed ribs indicate the CFD-adjoint reverse design is in accord with the theory that turbulence enhances heat transfer in the boundary layer. The Nusselt number of the novel ribs is averagely 1.9 times compared with the smooth. The THPP of the novel ribs approaches the local maximum at the design Reynolds number with the average THPP of 1.51.

Digital Twin for the Prediction of Extreme Loads on a Wave Energy Conversion System

Wave energy is a renewable energy source with the potential to contribute to the global electricity demand, but a remaining challenge is the survivability of the wave energy converters in harsh offshore conditions. To understand the system dynamics and improve the reliability, experimental and numerical studies are usually conducted. However, these processes are costly and time-consuming. A statistical model able to provide equivalent results is a promising approach. In this study, the digital twin of the CFD solution is developed and implemented for the prediction of the force in the mooring system of a point-absorber wave energy converter during extreme wave conditions. The results show that the digital twin can predict the mooring force with 90.36% average accuracy. Moreover, the digital twin needs only a few seconds to provide the solution, while the CFD code requires up to several days. By creating a digital analog of a wave energy converter and showing that it is able to predict the load in critical components during extreme wave conditions, this work constitutes an innovative approach in the wave energy field.

Numerical and experimental assessment of hydrodynamic force of a heaving porous disk

ABSTRACT The heave disk has been extensively employed as a motion damping device in floating offshore structures and inclusion of porosity on the disk further increases damping by generation of hole vortices. The present study explores the hydrodynamic forces of the solid and porous heave disk through numerical approaches and laboratory experiments. A simplified axisymmetric CFD model based on OpenFoam software is adopted here for numerical calculation. For verification of the numerical model, the laboratory test is conducted with the heave disk for different porosities and KC (Keulegan-Carpenter) numbers. The simplified CFD solutions are in good agreement with experimental results. It is observed that the porous disk with porosities of 0.049 and 0.11 shows maximum damping within the given range of KC numbers. From flow visualisation near porous disk, it is shown that as porosity increases, the increased flow through openings inhibits the formation of edge vortex.

Optimization of UAV Airfoil Based on Improved Particle Swarm Optimization Algorithm

Airfoil optimization is an essential task in the aerodynamic layout design of the unmanned aerial vehicle (UAV). An objective optimization function was constructed based on the airfoil power factor and handling stability at various attack angles. The parametric mathematical model of the airfoil and aerodynamic parameter proxy model of airfoil were constructed using the Hicks-Henne improved function and CFD solution sample, focusing on the issues with particle swarm optimization algorithms such as slow convergence, a tendency to fall into local optimal solutions, and oscillation at a late stage; an optimization method for the low-speed airfoil of a small UAV based on improved particle swarm optimization was developed. When compared to standard particle swarm optimization, selective regenerative particle swarm optimization, and improved particle swarm optimization, the results indicate that the maximum thickness of the optimized rear airfoil decreases from 19.77% to 18.76%, the number of iterations decreases from 112 to 31, and the search speed of the improved particle swarm optimization significantly improves; the CFD results indicate that the optimized rear airfoil exhibits superior aerodynamic performance. On average, the airfoil’s maximum lift-to-drag ratio is increased by 11.9%, its maximum power factor is increased by 12.5%, and its pitching moment is reduced by 8.4%. Within the UAV’s speed range, the aerodynamic performance is stable.

Numerical procedure for Pre-Swirl Stator structural integrity evaluation

This paper presents the numerical procedure for Pre-Swirl Stator (PSS) structural design with emphasis on wave induced hydrodynamic loads. The procedure consists of three main steps: definition of Dominant Loading Parameter (DLP), long-term wave statistical analysis leading to Equivalent Design Waves (EDWs) and non-linear simulations of defined EDWs. DLP is defined using simplified lift force approximation for airfoil profile. Non-linearity in the DLP definition requires the time development of each contributing sea-state from the scatter diagram and analysis of the signal to obtain proper statistical parameters for further long-term estimations. In the long-term wave analysis, potential flow is used due to its efficiency compared to more complex CFD method. Non-linear EDW simulations are performed with the CFD/FEM coupling model for a more realistic estimation of the loads and stresses. Extreme response and fatigue are assessed in this work with detail verification and explanation of each step in the entire procedure. Potential flow is solved by means of HydroStar, CFD solution is obtained using open-source tool OpenFOAM and FEM solution is obtained by means of NASTRAN. Overall, the results show that the proposed method can reliably predict the maximum expected wave loads and proves the current design of analyzed PSS to satisfy the extreme response and fatigue criteria.

Improved Prediction of Aerodynamic Loss Propagation as Entropy Rise in Wind Turbines Using Multifidelity Analysis

Several physics-based enhancements are embedded in a low-fidelity general unducted rotor design analysis tool developed, py_BEM, including the local Reynolds number effect, rotational corrections to airfoil polar, stall delay model, high induction factor correction, polar at large angle of attack, exergetic efficiency calculation and momentum-based loss. A wind turbine rotor is analyzed in high fidelity designed from py_BEM using a 3D blade generator. It is a design derived from the NREL Phase VI rotor. Three design variations are analyzed using steady 3D CFD solutions to demonstrate the effect of geometry on aerodynamics. S809 and NACA 2420 airfoil properties are used for calculating the aerodynamic loading. Momentum, vorticity and energy transport are explained in depth and connected to entropy production as a measure of performance loss. KE dissipation downstream of the rotor is shown to be a significant contributor of entropy rise. Wake analysis demonstrates mixing with the free stream flow, which begins after 3 diameters downstream of the rotor and extends to about 25 diameters until the decay is very small. Vorticity dynamics is investigated using a boundary vorticity flux technique to demonstrate the relationship between streamwise vorticity and lift generated in boundary layers. Drag components are accounted as well. It is demonstrated using rothalpy that shaft power is not only torque multiplied by rotational velocity but a viscous power loss term must also be included. A multifidelity analysis of wind turbine aerodynamics is demonstrated by capturing flow physics at several levels.

A Reliable Update of the Ainley and Mathieson Profile and Secondary Correlations

Empirical correlations are still fundamental in the modern design paradigm of axial turbines. Among these, the prominent Ainley and Mathieson correlation (Ainley D. and Mathieson G., 1951, “A Method of Performance Estimation for Axial-Flow Turbines,” ARC Reports and Memoranda No. 2974) and its derivatives, plays a crucial role. In this paper, the underlying assumptions of the aforementioned models are discussed by means of a descriptive review, whilst an attempt is made to enhance their reliability and, potentially, accuracy in performance estimations. Closer investigation reveals an intriguing misuse of the lift coefficient in the secondary loss. In light of this, an enhanced model that, notably, builds upon the Zweifel criterion and the vortex penetration depth concept is developed and discussed. The obtained accuracy is subsequently assessed through CFD computations, employing a database comprising 109 cascades. The results indicate a 50% probability of achieving the ±15% error interval, which is twice as good as the most recent Aungier model (Aungier R., 2006, “Turbine Aerodynamics: Axial-Flow and Radial-Inflow Turbine Design and Analysis”, ASME Press, New York). Furthermore, the reliability of the proposed model is demonstrated by a reconstruction of the Smith chart, on the one hand, and a performance analysis, on the other. The reconstruction exhibits contours that conform to the original. The results of the performance study are compared with the CFD solutions of eight cascades working in off design conditions and confirm the need of the additionally included turbine design parameters, such as the axial velocity and the meanline radius ratios.

Accuracy of Küchemann’s prediction for the locus of aerodynamic centres on swept wings compared to an inviscid panel method

AbstractThe locus of aerodynamic centres of a finite wing is the collection of all spanwise section aerodynamic centres, and depends on aspect ratio, wing sweep and planform shape. This locus is of great importance in the positioning of vortex elements in lifting-line theory. Traditionally, these vortex elements are placed along the quarter-chord of a wing, leading to inaccurate predictions of aerodynamic coefficients for swept wings due to the discontinuity in the line of vorticity at the wing root. An analytical solution was presented by Küchemann in 1956 to determine the locus of aerodynamic centres as a function of sweep. While experimental studies have been performed to visualise this locus, no large amount of data is available to fully evaluate the accuracy of Küchemann’s analytical solution. In the present study, a numerical approach is taken using a high-order panel method for inviscid, incompressible flow to calculate the locus of aerodynamic centres for elliptic wings over a wide range of sweep angles, aspect ratios and profile thicknesses. An inviscid panel method is chosen over full CFD solutions because of their ability to isolate the inviscid phenomena. Küchemann’s prediction is compared to this numerical data. The root mean square error is calculated for each wing in a broad design space to determine the accuracy of Küchemann’s theory. It is shown to be remarkably accurate over the range of cases studied, with the root mean square error staying below 4% for all wings with aft sweep and aspect ratios higher than $R_A=5$ . The actual difference between Küchemann’s prediction and numerical data is lower than that for the majority of the span for many of the wing designs considered, with the RMS error being skewed by the results at the tip. Results demonstrate that Küchemann’s analytical equations can be used as an accurate approximation for the locus of aerodynamic centres and could be used in modern numerical lifting-line algorithms*.

Reduced-order model for efficient generation of a subsonic missile’s aerodynamic database

AbstractThis article reports on the development of a fast method for generating the aerodynamic database for subsonic flow over a missile. At present, this is typically achieved using RANS-based CFD, which is expensive for the complex missile geometries and the multiplicity of operating conditions to be evaluated. The presented reduced-order model (ROM) provides a reasonably accurate prediction of the aerodynamic coefficients of the missile (and, in fact, the full flow field around it) within half a minute. In particular, in the interpolative regime, prediction errors for all coefficients are typically less than 1% of their respective maximum values encountered in the database, with extrapolation incurring more error. The empirical approach ‘learns’ from the CFD solutions calculated for a few operating conditions, and then is able to make predictions for any other condition within a feasible set. The learning employs proper orthogonal decomposition (POD) to characterise the most important features of the flow. The prediction is posed as an optimisation problem that aims to find the flow solution as a linear combination of the above POD modes that minimises the residual of the governing equations. Innovations on the prevailing POD-ROM approach include novel implementation of boundary conditions, simplified computation of the aerodynamic coefficients, and a procedure for choosing modelling parameters based on extensive cross-validation. Challenges overcome in application to a problem of industrial relevance are discussed.

Automatic determination of coupling time step and region in unresolved DEM-CFD

When unresolved CFD-DEM is used in coupling calculation, both fluid flow field and particles dynamic both are in time and space domains solves. The coupling time step (coupling number) and coupling region (CFD solution domain) directly affect calculation accuracy and efficiency. Therefore, through real-time update of coupling conditions, establishment of CFD global as well as sub-domain solution technology, we proposed a calculation method for automatically determining the coupling time step and region. Our proposed strategy reduced the solution scale of the fluid domain during coupling, controlled coupling calculation accuracy, and improved calculation efficiency. The calculation revealed that maximum errors of displacement and velocity of single particle settling motion in a finite fluid were 6.2% and 7.1%, respectively, while maximum efficiency was improved by 44.4%. The maximum error reached 3.9%, when the velocity of particles in the pipe was 3.5 m/s. Computational efficiency increased by 26.1%.

Nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. In this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

Focus boom simulation benchmark cases for the 182nd ASA Meeting May 2022

The low-boom prediction committee comprised of several research agencies and companies across the world plans to organize a special session dedicated to prediction and comparison of focused sonic booms. This presentation will document and discuss the benchmark cases that will be studied and compared during this special session. The case description would include the underlying near-field CFD data along with relevant flight conditions and mission trajectory information for the participants to simulate and discuss their individual focus boom predictions. Details of the CFD simulation conditions and solution procedure to obtain off body pressure waveforms on a cylindrical surface around the aircraft at a few selected points along the flight trajectory will be provided. The rationale for the choice(s) of the mission trajectories to result in focus booms near the ground for comparison using multiple independent implementations will be provided as well.

Numerical assessment of a two-phase Tesla turbine: Parametric analysis

• Tesla turbine performance analysis in two-phase condition via CFD and analytical model. • The phase change model is adapted to R404a based on saturation temperature. • 1D-homogeneous analytical model estimation is comparable with 3D nonhomogeneous model. • The surface roughness effect is more pronounced at lower gaps between the disks. • The two-phase tesla turbine produced ~ 0.8 W and torque of 3.6 mN-m at 2000 RPM. The scenarios on the future energy systems invariably point to heat pumps as an emerging technology to reach efficiency goals alongside energy and CO 2 reduction targets. Moreover, they may progressively foster the use of chillers and refrigeration units. In this study, a technology that could enhance the efficiency of systems based on inverse cycles is analysed. Particularly, the two-phase flow behaviour of a Tesla turbine is numerically investigated. The main objectives are to clarify the role of the second phase, the actual operating range, and examine the flow mixing. Two computational approaches are developed, relying on a customised home-built mathematical model and CFD analyses carried out with a commercial software. The calculations are performed for two-phase R404a fluid over significant ranges of rotational speed, plate gap size, and plate roughness. All the critical liquid–vapour interactions are determined and discussed utilising the CFD solution of the Eulerian-Eulerian approach with a frame motion technique. The other model is a homogeneous finite-difference solution, and the mass transfer is directly determined based on the phase diagram of the fluid neglecting other phase-interaction parameters. The two approaches are compared to some available experimental results from the literature, revealing an excellent agreement. The results show the average power output of 0.8 W with a delivered torque of 3.6 mN-m at a rotational speed of about 2000 RPM. The numerical analysis explains the different effects of the two-phase conditions on the turbine efficiency, paving the way to an accurate design of boundary layer turboexpanders operating under these conditions.

Unsteady continuous adjoint to URANS coupled with FW-H analogy for aeroacoustic shape optimization

In this paper, an unsteady aeroacoustic shape optimization tool is presented based on the continuous adjoint method. Aeroacoustic noise radiated by bodies in unsteady flows can be computed using a hybrid acoustic prediction tool, where the near-field flow and acoustics result from an unsteady CFD simulation while the acoustic propagation to far-field relies upon an acoustic analogy. The CFD solution is performed using the in-house GPU-enabled unsteady RANS solver for which a continuous adjoint solver is also available. Next to this, the noise prediction tool is developed based on the permeable version of the Ffowcs Williams and Hawkings analogy in the frequency domain and its implementation is verified by comparison to a well-known analytical solution of the sound field from a monopole source in uniform flow as well as comparing the results computed by the FW-H analogy with that of a time-accurate CFD run. The full mathematical formulation of the continuous adjoint method for the aforementioned acoustic analogy, coupled with the adjoint to the mean-flow and turbulence model equations, is presented. The accuracy of the gradients computed by the hybrid adjoint method is verified through comparisons with finite differences in two cases, both governed mainly by the tonal component in noise generation; these include the vortex shedding cylinder in a laminar flow and the rod-airfoil canonical benchmark in a turbulent flow. Finally, the programmed software is used to optimize the shape of the airfoil in the last test case, aiming at min. noise for a receiver located at far-field.

Deciphering the optimal exergy field in closed-wet cooling towers using Bi-level reduced-order models

This paper introduces a bi-level reduced-order models (ROMs) approach for quickly deciphering the optimal exergy fields in closed wet cooling towers (CWCTs) with consideration of weather variations. First, an efficient sampling method based on stochastic reduced-order model is performed for the approximation of the multivariate probability distributions by generating a finite set of samples. The uncertainty associated with input variables is propagated via multi-sample CFD simulations of the CWCT model for each of the samples. The results of the state and output variables stored in the CFD solutions are used to construct the data-driven and physics-based ROMs by combining principal component analysis and artificial neural network methods. The constructed data-driven ROM is embedded in a sampling-based stochastic optimization model that seeks the maximization of the expected exergy efficiency ratio. The physics-based ROM is used to visualize the optimal field profiles of the thermal-, mechanical-, and chemical-exergy fluxes. Finally, the results of a case study demonstrate that the main strengths of the proposed approach is to simultaneously obtain the optimal exergy efficiency ratios and the exergy field profiles of the CWCT system in a computationally efficient manner.

A hydrodynamic basis for off-axis Brownian diffusion under intermediate confinements in micro-channels

The mobility of a Brownian particle diffusing in a micro-channel is heterogeneous and spatially dependent on the surrounding hydrodynamic resistance fields. The positional asymmetry of such a diffusing particle leads to anisotropies in the observed diffusive behavior. In this paper, we probe such directionally varying diffusive behavior of a spherical nanoparticle diffusing at a location off-set from the centerline of a square micro-channel in a quiescent fluid. This investigation is carried out over varying degrees of intermediate hydrodynamic confinements. A coupled Langevin-immersed boundary method is used for these assessments. We observe that the co-axial diffusivity may be slightly enhanced during off-axis hindered diffusion when compared with a corresponding centerline diffusive behavior. We attribute this increased particle diffusivity to a reduced co-axial fluid resistance through a hydrodynamic basis derived using steady-state CFD solutions to the corresponding Stokes problem. For co-axial motion, the particle creates a recirculating flow pattern around itself when moving along the centerline, whereas it drags along the fluid in between itself and the wall when in close proximity to the latter. These contrasting flow behaviors are responsible for the unexpected enhancement of the co-axial diffusivity for some off-axis positions under intermediate hydrodynamic confinements.

Obtaining pseudo-OH* radiation images from CFD solutions of transcritical flames

The quantitative comparison of experimental data and results from CFD simulations is still an ongoing challenge in the investigation of high pressure combustion in rocket combustion chambers. This is due to the extreme environment which develops in liquid propellant rocket engines, which represent a challenge for experimental data collection. OH* radiation emitted from the flame has often been designated as an indicator of the combustion zone, because of its relative ease of detection with appropriate cameras. A method was developed to compare OH* radiation originating from cryogenic oxygen-hydrogen flames in an experimental combustor with the CFD simulation results. Pseudo-OH* images were obtained from CFD results of two combustors. The method consists in obtaining the path of a ray of light by a reverse ray tracing algorithm and sampling the thermodynamic properties along the path of the ray, simulating the emission and absorption spectra in the wavelength range of interest, in this case of OH* emission during combustion. The spectral radiance is then determined by solving the differential radiative transfer equation. Finally, the total radiance is calculated integrating the spectral radiance. The results obtained applying this method are then compared with former results of two test cases, a laminar and a turbulent flame, and with the related experimental data. An improvement of the comparison with the experimental data was achieved in terms of the prediction of self-absorption, which was underestimated in previous works by a factor of 15, and in terms of radiance near the injection plane, where difference is estimated to be about 40% when including refraction. The method allows for more direct comparison between 3D CFD results and 2D experimental images collected by the optical setup and probes.

CFD Modelling of Non-Newtonian Fluid Flow in a Pipe Including Obstacle

Pipe flow problems are important in transportation of wastewater, oil lines and supply of water. In this study, a non-Newtonian fluid model is discussed and a numerical CFD solution is presented for flow geometry. The effects on velocity, pressure, dynamic viscosity and cell Reynolds number are discussed for different parameters of flow inside the pipe. Power Law function is considered in the analyses.

VPP Coupling High-Fidelity Analyses and Analytical Formulations for Multihulls Sails and Appendages Optimization

A procedure for the optimization of a catamaran’s sail plan able to provide a preliminary optimal appendages configuration is described. The method integrates a sail parametric CAD model, an automatic computational domain generator and a Velocity Prediction Program (VPP) based on a combination of sail RANS computations and analytical models. The sailing speed and course angle are obtained, with an iterative process, solving the forces and moment equilibrium system of equations. Analytical formulations for the hull forces were developed and tuned against a matrix of CFD solutions. The appendages aerodynamic polars are estimated by applying preliminary design criteria from aerospace literature. The procedure permits us to find the combination of appendages configuration, rudders setting, sail planform, shape and trim that maximise the VMG (Velocity Made Good). Two versions of the sail analysis module were implemented: one adopting commercial software and one based on the use of only Open-Source codes. The solutions of the two modules were compared to evaluate advantages and limitations of the two approaches.