CFD Solutions Research Articles

Enhanced Drag Force Estimation in Automotive Design: A Surrogate Model Leveraging Limited Full-Order Model Drag Data and Comprehensive Physical Field Integration

In this paper, a novel surrogate model for shape-parametrized vehicle drag force prediction is proposed. It is assumed that only a limited dataset of high-fidelity CFD results is available, typically less than ten high-fidelity CFD solutions for different shape samples. The idea is to take advantage not only of the drag coefficients but also physical fields such as velocity, pressure, and kinetic energy evaluated on a cutting plane in the wake of the vehicle and perpendicular to the road. This additional “augmented” information provides a more accurate and robust prediction of the drag force compared to a standard surface response methodology. As a first step, an original reparametrization of the shape based on combination coefficients of shape principal components is proposed, leading to a low-dimensional representation of the shape space. The second step consists in determining principal components of the x-direction momentum flux through a cutting plane behind the car. The final step is to find the mapping between the reduced shape description and the momentum flux formula to achieve an accurate drag estimation. The resulting surrogate model is a space-parameter separated representation with shape principal component coefficients and spatial modes dedicated to drag-force evaluation. The algorithm can deal with shapes of variable mesh by using an optimal transport procedure that interpolates the fields on a shared reference mesh. The Machine Learning algorithm is challenged on a car concept with a three-dimensional shape design space. With only two well-chosen samples, the numerical algorithm is able to return a drag surrogate model with reasonable uniform error over the validation dataset. An incremental learning approach involving additional high-fidelity computations is also proposed. The leading algorithm is shown to improve the model accuracy. The study also shows the sensitivity of the results with respect to the initial experimental design. As feedback, we discuss and suggest what appear to be the correct choices of experimental designs for the best results.

Mathematical theory and CFD solutions for internal convective cooling of gas turbine blades highlighting the effects of rotation

A quasi-one-dimensional mathematical theory is developed for determining the effects of rotation on the fluid flow and heat transfer in a cooling channel within a rotating gas turbine blade. The three-dimensional intricacies in the solutions of the same problem are captured through accurate computational fluid dynamic simulations. The derived analytical closed-form solutions predict the amount by which the relative total temperature of the coolant changes as a result of rotation. It is shown that such changes due to rotation are significant proportion of the change of coolant temperature due to heat transfer. The computed spatial evolutions of the primary velocity field, secondary velocity field and the force fields are presented as the coolant progresses from the inlet to the outlet so that the complexities and subtleties are exposed to a high degree of visualizability. Detailed considerations to various components of the centrifugal, Coriolis and pressure forces are given. The flow field is shown to depend strongly on whether the coolant moves in the spanwise outward or inward direction. The three-dimensionality of the flow field is reflected in complex circumferential variations of the blade temperature and the internal heat transfer coefficient. When the effects of the x–component of the Coriolis force interacts non-linearly with the effects of the z–component of the centrifugal force and a drastic x-gradient in fluid density due to a thin thermal boundary layer, then the primary velocity profile may exhibit great complexity, including flow separation. The present paper thus captures the strong, non-linear, two-way coupling between the fluid dynamics and heat transfer in the internal convective cooling occurring in a channel within a rotating gas turbine blade. Based on about 100 three-dimensional computational fluid dynamics simulations, new heat transfer correlations are developed for average Nusselt number for a rotating channel that will be of practical use.

Machine learning of unsteady transonic aerodynamics of a pitching truss-braced wing section

A detailed analysis of transonic aerodynamics of a pitching conceptual Boeing Truss-Braced Wing (TBW) section has been carried out at various Mach numbers at a typical reduced frequency, k = 0.15. A new important flow feature of hysteresis loop cross-over has been discovered through the analysis of the cl hysteresis loops. Transonic dip has been located at M = 0.87, where the mean cl attains a minimum value. Hysteresis loop cross-over and transonic dip are important in the transonic flutter analysis of these wing sections. High fidelity database for the TBW section corresponding to different M in the range [0.7 - 0.9] has been generated by numerically solving the Navier-Stokes equations on a supercomputer at the NASA Advanced Supercomputing Division. A regularization-based machine learning (ML) methodology has been developed to predict the transonic aerodynamics of the pitching TBW section, using the training data as a subset of this high fidelity database. The ML model was then tested on test data as a subset of this database exclusive of the training data. Each ML model prediction is achieved well within a minute of computing time, as opposed to tens of hours of super-computing time required for each high fidelity CFD solution, thus making it a feasible tool for the design of a TBW, with the wing flutter in perspective. The TBW section flow was simulated corresponding to an altitude of 44,000 ft.

A space marching method for sonic boom near field predictions

The conventional sonic boom propagation prediction method widely adopted in supersonic aircraft design involves a two-step procedure. In the first step, a compressible viscous or inviscid Computational Fluid Dynamics analysis is applied to the aircraft geometry at flight conditions to produce a flow field solution near the aircraft. Then in the second step, a one dimensional nonlinear Burgers’ equation model is used to propagate sonic boom signature traces from the near field solution at flight altitude to the ground along a ray path. For an accurate ground signature prediction the near field signature must be accurately modeled at a sufficient distance from the aircraft flight path in order to minimize errors in the one dimensional propagation model. This is a very challenging task for general purpose CFD tools in a design environment because the cost of maintaining highly accurate off-body solutions increases dramatically as the radial distance is enlarged in the computational domain. It is also particularly difficult to apply these tools for wave propagation because the algorithms are normally lower order and numerically dissipative and dispersive. In this work a space marching procedure based on an optimized higher order finite difference method is developed and applied in conjunction with a CFD solution concentrated in the close vicinity of the aircraft. This new approach is much more efficient, compared to previous methods, in providing highly accurate near field signatures for full carpet ground predictions. Results indicate that near field signatures retain more waveform shape information farther from the aircraft geometry while reducing the CFD cost significantly. The predicted ground signature is also shown to converge in shape as the radial distance of the near field signature grows, which is indicative of a more ideal initial condition being supplied to the one dimensional wave propagation to ground. This feature is very difficult to replicate in a tractable manner with common CFD approaches used in design.

Three-dimensional Effects on Gap-Resonances in Twin-Hull Vessels in Time-Harmonic Vertical Oscillations

Three-dimensional effects induced by dimensional ratios on the gap resonances happening in twin hull vessels oscillating in forced vertical motion have been analyzed. They can lead to relevant consequences, such as the amplification of the inner radiated waves or the generation of standing waves in between the demi-hulls, that can have a direct effect on the operating profile of the vessel. The response of twin hull vessels in waves can be strongly affected by these resonant phenomena. Also, some of these behaviors can be exploited in the framework of wave energy conversion systems. The present analysis is carried out by using an open-source, linear, Boundary Element Method (BEM), based on the Green function approach. Mathematical backgrounds of the added mass and damping coefficients computation for a floating body under harmonic vertical oscillation are provided as well as details of the numerical discretization used in the BEM. A panel mesh sensitivity study is carried out and the numerical prediction is validated by comparison against available experimental data, another CFD solution obtained by a high-fidelity viscous solver based on the open-source libraries Open-FOAM and approximate analytic formulations. The effect of the beam ratio and the length-to-beam ratio on the resonant phenomena has been analyzed. This has been achieved by systematic variations of the geometric dimensions of the hull, focusing on the trends of the hydrodynamic coefficients, the amplitude of the radiated waves, and the location of the resonant frequencies over the analyzed range.

An Implementation of LASER Beam Welding Simulation on Graphics Processing Unit Using CUDA

The maximum number of parallel threads in traditional CFD solutions is limited by the Central Processing Unit (CPU) capacity, which is lower than the capabilities of a modern Graphics Processing Unit (GPU). In this context, the GPU allows for simultaneous processing of several parallel threads with double-precision floating-point formatting. The present study was focused on evaluating the advantages and drawbacks of implementing LASER Beam Welding (LBW) simulations using the CUDA platform. The performance of the developed code was compared to that of three top-rated commercial codes executed on the CPU. The unsteady three-dimensional heat conduction Partial Differential Equation (PDE) was discretized in space and time using the Finite Volume Method (FVM). The Volumetric Thermal Capacitor (VTC) approach was employed to model the melting-solidification. The GPU solutions were computed using a CUDA-C language in-house code, running on a Gigabyte Nvidia GeForce RTX™ 3090 video card and an MSI 4090 video card (both made in Hsinchu, Taiwan), each with 24 GB of memory. The commercial solutions were executed on an Intel® Core™ i9-12900KF CPU (made in Hillsboro, Oregon, United States of America) with a 3.6 GHz base clock and 16 cores. The results demonstrated that GPU and CPU processing achieve similar precision, but the GPU solution exhibited significantly faster speeds and greater power efficiency, resulting in speed-ups ranging from 75.6 to 1351.2 times compared to the CPU solutions. The in-house code also demonstrated optimized memory usage, with an average of 3.86 times less RAM utilization. Therefore, adopting parallelized algorithms run on GPU can lead to reduced CFD computational costs compared to traditional codes while maintaining high accuracy.

Method of characteristics for transient, planar, cylindrical flows

Cylindrical radiation of individual pulses is studied and strong differences from spherical radiation are highlighted. Prior to this study, the class of available analytical solutions for cylindrical radiation was rather limited. It included (i) a well-known solution for a steady-state, time-harmonic line source and (ii) the solution for a delta-pulse line source. The first of these has no analytical counterpart for individual pulses. By means of the second (actually the Green's function) a more general class of line source solutions can be formulated, but each one is in the form of an integral that has to be evaluated numerically and requires tedious preparation of a singular integrand, making it difficult to achieve perfect accuracy. In the present paper, use is made instead of a particular family of analytically-exact (linear) solutions that has been developed recently. It is used to assess the accuracy of solutions obtained numerically by the method of characteristics (MoC), which is then applied to more general sources than those amenable to analytical treatment. The MoC analysis is specially formulated to reduce the influence of terms involving the reciprocal of the radius (such terms are numerically unmanageable close to the origin). It is found that the qualitative behaviour of waves radiating from the surface of a cylinder of finite radius can depend strongly on the duration of the initiating disturbance and that this can be interpreted in a convolution-like manner. After validation, the numerical method is coupled with a conventional MoC analysis of planar wave propagation and is used to simulate the reflection and radiation of an initially planar wavefront arriving at a flanged duct exit. The numerical representation is one-dimensional in both domains – (x,t) inside the duct and (r,t) outside it. Although its use implies identical behaviour in all radial directions in the external domain, the solution is found to be in close agreement with circumferential-average values from a CFD solution that simulates azimuthal variations as well as radial variations. Whilst being less comprehensive than the CFD simulation, the MoC analysis has the important practical benefit of making highly efficient use of human and computational resources. By comparing the MoC and CFD solutions, it is found that the nominally-cylindrical radiation from the duct approximates closely to radiation from a line source a small distance inside the duct (not at the exit plane). An approximate location of the effective source is quantified.

Three-dimensional optimization of squealer-tip for a transonic axial-flow compressor rotor blade

This research represents an innovative method for geometry generation of the squealer-tip in axial compressor rotors and its exploit in a numerical optimization process to obtain a better stage performance. For this purpose, the NASA Rotor-67 transonic compressor rotor blade is used as a test case to study the aerodynamic performance using computational fluid dynamics. The validation was performed for the characteristic map at the design speed and the comparison with the experimental results indicates excellent matching and high adaptability of the numerical method. An ingenious method of producing squealer tip for an axial compressor rotary blade is presented in this article, which is capable for locally shaping both suction and pressure surface geometry at a desired spanwise location simultaneously, while keeping the tip clearance at its value of the baseline NASA Rotor-67 geometry. In this method, control points are used to produce the starting spanwise location of the squealer, and modify the depth of the squealer geometry. The L-27 orthogonal array of the Taguchi method as the Design of Experiment (DOE) has been used to investigate the sensitivity of the aerodynamic results in three performance points of the choke, design and near stall regions, in relation to the design variables of the squealer. The generated database in the sensitivity analysis was used to train artificial neural networks to replace the CFD solutions with overwhelming run time. By coupling the genetic algorithm to the aforementioned neural networks and by applying penalties to maintain the minimum performance of the Rotor-67, enhancement of total pressure ratio, adiabatic efficiency, mass flow rate and even the surge margin was achieved. The main effect of the squealer is to modify the shape of blade tip vortices, and by more dissipation of energy in blade tip area and reduced equivalent flow area in this region, finally results in improved overall mass flow rate, total pressure ratio, adiabatic efficiency and surge margin by 0.58 %, 0.36 %, 0.19 % and 4.81 % respectively, at design point.

NUMERICAL ANALYSIS AND DIFFUSER VANE SHAPE OPTIMIZATION OF A RADIAL COMPRESSOR WITH THE OPEN-SOURCE SOFTWARE SU2

In recent years, the usage of open-source computational fluid dynamics tools is on a rise both in industry and academia. SU2 is one of these open-source tools. Unlike other open-source alternatives, SU2 is equipped with boundary condition types, solvers and methods that are especially developed for the analysis and design of turbomachinery. The aim of this work is to explore and investigate the capabilities of SU2 in the prediction of performance parameters of radial compressors. Two different single stage shrouded compressor geometries, one with a vaneless diffuser and the other with a vaned diffuser have been investigated with steady state CFD. The compressors were designed by MAN Energy Solutions Schweiz AG. Computational results with SU2 showed a satisfactory agreement with both the experimental data and reference CFD solutions obtained with Fidelity Flow, which is formerly known as Numeca Fine TURBO. Only at the relatively higher mass flow rates the difference between references and SU2 were higher compared to other operating points. After performance parameters were successfully calculated with SU2, the optimization tools that come with SU2 were also used. A 2D adjoint optimization study on the vane of the vaned diffuser was carried out. The study was carried out at a single operating point that is close to choke conditions. The loss generated by the large separated flow region at the suction side of the diffuser vane was reduced by 0.55 % in the optimized geometry using minimal modifications on the existing vane geometry to keep the performance of the compressor intact at other operating points. However, the resulting modification increased the total pressure loss by 0.86 % at one of the design operating points. This performance penalty could be due to the discontinuity in the vane geometry generated by the optimizer. Overall, the study shows that SU2 has the basic numerical schemes and models that are required for the analysis of radial turbomachinery flows and geometry optimization.

Enhanced heat dissipation of ribbed channels based on the coupling optimization of multiple structural parameters

The heat dissipation of ribbed channels is dominant by the strong coupling of multiple structural parameters, while it is less concerned due to the lack of efficient methodology both in experimental and numerical solutions. In the present work, the movable experimental facility and the CFD solutions based on the conjugate gradient method are established. Firstly, the coupling impacts of different parameters on the airflow field in the channel are identified. It is found that the longitudinal vortices coupling with transverse secondary flows are in charge of the heat dissipation of the ribbed channel. And the longitudinal vortices are affected by the relative roughness spacing, and the transverse secondary flow is mainly dependent on the aspect ratio for L-shaped rib, while for the V-shaped and W-shaped ribs, the transverse secondary flow mainly is mainly dependent on the angle of attack. Secondly, the coupling optimization of different ribs is completed and the optimal structural parameters are obtained using the developed experimental and numerical methodology. Overall, compared with the smooth channel, the optimal L, V and W-shaped ribs deliver the Nusselt number increasing by 83.04%, 155.18% and 197.17%.

A dual-solver CFD model for conjugate heat transfer in continuous thermal processing

High temperature heat treatment of powders is a common operation in the manufacturing of a range of commercial products. Often, powders are heated or cooled in discrete quantities while being conveyed through a continuous furnace or oven, where a certain temperature–time profile is required for product quality reasons. For powders that are contained and conveyed in oven-ware (saggars), heat-transfer occurs between the surrounding gas phase and the powder material and oven-ware, as well as between oven ware that is vertically stacked.The large physical size and long transit times through typical industrial furnaces (up to 40 m length) means that a full transient CFD solution for both gas and solid phases is computationally very expensive . In this study, a novel CFD simulation model is developed for conjugate heat transfer in the cooling section at the outlet of a continuous furnace. A particular novel feature in this model is the inclusion of heat conduction in multiple solid domains. A dual-solver approach enables the convective and radiant heat-transfer processes in the gas phase are modelled using a steady-state conjugate solver, while the heat conduction processes within the powders and saggars are modelled using a time-dependent conjugate solver that solves for heat conduction only. Using only steady-state solution for the gas phase enables a “snap-shot” of the thermal performance of the system to be generated in a reasonable time frame, which has practical implications for modelling of large-scale industrial equipment. In the “dual-solver” approach, heat fluxes at solid boundaries from the steady-state model are applied as boundary conditions to the transient solver, while the temperature field resulting from the solution of the transient solver is then applied to the steady-state model. Radiative cooling effects are accounted for using a discrete-ordinates model.

Investigation of nano composite heat exchanger annular pipeline flow using CFD analysis for crude oil and water characteristics

This study focuses on the dual-core annular process of crude oil and water. The crude oil exhibits non-Newtonian behavior with high viscosity. The heat transmission flow in pipeline locations is complex. In this process, the cooled water passes through the annular core, experiencing turbulence effects, while the crude oil flows in a laminar manner. The influence of the non-Newtonian behavior is investigated in terms of pipe angles and deformations. In the valve, the inlet velocity flow is set at 1.75 m/s. The flow is executed in downhill orientations in high-velocity locations. The simulation results show CFD variations with a velocity of 3.5 m/s, pressure of 2.33 MPa, pressure gradients of 1.33 MPa, and Reynolds numbers of 1.38 MPa. This study is being conducted for a horizontal pipeline. The CFD solution solvers investigate the volumetric flow characteristics of the fluid as well as the temperature effects. The maximum heat energy has been reduced, resulting in unique flow directions.

Modelling green water loads on ships using coupled impulse response function and CFD solution

A 3D coupled method is used to model green water and to study numerically the influence of wavelength, wave steepness, and bow rake angle on the green water occurrence and peak pressure on a ship deck. To do that, the global motions of the vessel are obtained in the time domain using an impulse response function. The local hydrodynamic forces of green water load are computed using a commercial CFD solver together with the Volume of Fluid method. The approach is validated using in-house experimental results. Then a systematic parametric study is performed to understand the effect of several geometric and environmental parameters on green water loads. The results indicate that peak pressure due to green water increases significantly with vessel speed for all the wavelengths investigated and decreases with the increase of bow rake angle.

High-fidelity aerodynamic and acoustic design and analysis of a heavy-lift eVTOL

This work presents the high-fidelity aerodynamic and acoustic modelling processes supporting the preliminary design of a large eVTOL vehicle at the University of Glasgow in collaboration with GKN Aerospace. To support the GKN heavy-lift eVTOL design, known as Skybus, a range of tools of various fidelity levels were adopted and integrated. This paper first presents the conceptual design and initial sizing of the Skybus vehicle. The airframe design was then analysed using high-fidelity methods with parametric variations of wing an/di-hedral designs. By adjusting the interactions between the wings and the airframe, 5∘ front wing anhedral combined with 10∘ aft wing dihedral offered the maximum lift increase. High-fidelity CFD simulations of the complete Skybus vehicle in forward flight with two and four operating propellers were later carried out. The aerodynamic interactions between the propellers and the wings were analysed in detail. In cruise, the four-rotor configuration showed stronger aerodynamic interference effects and hence required more power than the two-rotor counterpart. Near-field acoustics of the vehicle was then extracted directly from the flow solutions and analysed. Far-field noise features were also computed using the FW-H equations and the CFD solutions. The peak noise levels of the heavy-lift vehicle in forward flight at 90 m/s were about 75 dB SPL perceived on the ground 1000 m below. Acoustic features and differences of the two configurations along the flight path and in the lateral directions were presented and discussed.

A Study on the Thermal Properties of Oil-Film Viscosity in Squeeze Film Dampers

Considering the variation in temperature of the oil film in squeeze film dampers (SFDs) caused by squeezing, a more comprehensive analysis of SFD can be obtained. Aiming to investigate the viscosity thermal effect of the oil film in SFDs, this study established a 3D CFD solution model. Based on the total energy model, the viscosity thermal effect was performed. With the mixture multi–phase flow model, the Zwart–Gerber–Belamri (Z–G–B) cavitation model, and the use of the additional mass coefficient, the two–phase flow phenomenon in SFDs was discussed. The oil film at various temperatures and the temperature distribution of different oil types under different working conditions were analyzed. Furthermore, the influence of the SFD thermal effect on the two–phase flow phenomenon were particularly carried out. Meanwhile, the simulation results of the SFD thermal effect were experimentally verified. The results revealed that the maximum temperature of the SFD oil film was enhanced with the increase in the eccentricity ratio and precession frequency. The temperature of the oil film was closely related to the oil dynamic viscosity. The dynamic viscosity of the oil was reduced, which was caused by the SFD thermal effect, thus leading to decreased oil–film damping, enlarging the vaporization level and the range of vapor cavitation, as well as the ingested air amount. CFD simulation results of the thermal effect were in good agreement with the experimental data, which verified the accuracy of the proposed model.

A data-driven adversarial machine learning for 3D surrogates of unstructured computational fluid dynamic simulations

This paper presents a general workflow to generate and improve the forecast of model surrogates of computational fluid dynamics simulations using deep learning, and most specifically adversarial training. This adversarial approach aims to reduce the divergence of the forecasts from the underlying physical model. Our two-step method integrates a Principal Components Analysis (PCA) based adversarial autoencoder (PC-AAE) with adversarial Long short-term memory (LSTM) networks. Once the reduced-order model (ROM) of the CFD solution is obtained via PCA, an adversarial autoencoder is used on the principal components time series. Subsequentially, a LSTM is adversarially trained on the latent space produced by the PC-AAE to make forecasts. Here we show, that the application of adversarial training improves the rollout of the latent space predictions. Our workflow is applied to three different case studies including two models of urban air pollution in London.

Extended scaling approach for droplet flow and glaze ice accretion on a rotating wind turbine blade

This paper presents and analyzes a non-dimensional model of the flow field and droplet trajectories with glaze ice accretion on a rotating wind turbine blade. The formulation leads to similitude relationships for glaze ice accretion to evaluate new scaling parameters corresponding to the rotation of the blade. New scaling parameters are developed to determine ice scaling conditions based on the geometry scale factor of a wind turbine blade. The scaling methodology can be used to determine alternative test conditions and predict glaze icing conditions on a full-scale wind turbine blade. Numerical CFD icing simulations are performed using ANSYS FENSAP ICE software. A wind blade model is developed using blade element momentum theory (BEM). Each blade size is tested at specific flow conditions using the scaling equations. Scaled conditions for velocity (streamwise and rotational), droplet size, and icing time are tested. CFD solutions for the flow field are obtained for comparisons of the velocity, droplet trajectories, pressure coefficient distributions, ice thickness, and ice shapes. Recommended parameters to be used for glaze ice scaling on a rotating blade are presented and numerical results are reported to support these recommendations. The paper provides new insights into modeling of glaze ice accretion on large wind turbine blades based on smaller scaled blade sections tested in a laboratory setting.

Hybrid CFD-ANN approach for evaluation of bio-inspired dolphins dorsal fin turbulators of heat exchanger in turbulent flow

The central aim of the present investigation is to evaluate the effects of bio-inspired Dolphin’s dorsal fin turbulators (DFTs) with a hybrid CFD-ANN approach in a counter flow double pipe heat exchanger. The DFT’s physical model is adapted from the infrared thermal image of a bottlenose dolphin dorsal fin. The effects of different influential parameters, such as the length scale (D) of DFTs including 4, 8, 12 mm and the number of turbulators (N) including 6, 10, and 14 are numerically examined at different Reynolds numbers. Also, using CFD data, the neural network is trained with great accuracy of R2 above 0.999. Important parameters such as Nu, f, Ɛ, NTU can be predicted in different conditions by the ANN method. This method greatly reduces the costs of CFD solutions, which is advantageous. The results indicate that the DFT's streamlined geometry could significantly reduce friction loss by streamlining the fluid flow. Also, colliding the fluid stream with the DFTs improves heat transfer by boundary layer destruction. The UA Ratio (UAR) of the Dolphin’s dorsal fin turbulator heat exchanger (DFTHE) to the simple heat exchanger (SHE) is between 1.02 and 1.74. Also, the ratio of Nu, Ɛ, NTU for the DFTHE to the SHE is equal to 2.48, 1.63, and 1.74, respectively.

INVESTIGATING THE EFFECTS OF OUTLET PRESSURE FROM STEAM TURBINE BLADE ON WETNESS AND ENTROPY GENERATION WITH CONSIDERATION OF NON-EQUILIBRIUM CONDENSATION

Steam turbines are one of the main elements of a power plant that steam thermal energy turns into rotational energy. Due to condenser pressure changes, the pressure at the end of steam turbines changes. In this study, the Bakhtar blade is used, and the effects of changes in the pressure outlet of the blade on the flow behavior are investigated. In this research, 62.56 kPa, 72.56 kPa, 82.56 kPa, 92.56 kPa, and 102.56 kPa are considered for the pressure at the end of the steam turbine blade. First, the CFD solution results are compared with the laboratory data of the Bakhtar turbine's blade. Then, the effect of outlet pressure is examined. Regarding obtained results, the proposed numerical solution can properly predict the experimental data. By the growth of the outlet pressure of the steam turbine blade, the Mach number decreases and the pressure and temperature distribution increase. As the pressure increases from 62.56 kPa to 102.56 kPa, the average Mach number decreases by 29.8% at the outlet, and the average temperature at the outlet increases by 3.9%. The nucleation rate does not have a noticeable change. However, liquid mass fraction decreases with the increase in outlet pressure. By increasing the pressure from 62.56 kPa to 102.56 kPa, the average wetness decreases by 39.5% at the outlet. This study shows that condenser pressure changes affect the liquid phase produced in the end blade of the steam turbine.

Scaling formulation of multiphase flow and droplet trajectories with rime ice accretion on a rotating wind turbine blade

In this paper, scaling and similitude are investigated for ice accretion on a rotating wind turbine blade. Numerical CFD icing simulations are performed using FENSAP ICE software to test the scaling methods and verify the results. A small blade section is scaled six times, and each case is tested at specific flow conditions. Scaled conditions for velocity (streamwise and rotational), droplet size, and icing time are examined. CFD solutions for the flow field (air and droplet) are obtained in terms of the velocity, droplet trajectories, pressure coefficient distributions, ice thickness, and ice shapes, by quantifying the significant parameters involved in the icing process. Recommendations for parameters to be used for rime ice scaling on a rotating blade are presented, and numerical results are reported to support those recommendations. Numerical results and test conditions are obtained at sea level in wind tunnel facilities for experimental investigation. This paper presents the formulation of non-dimensionlized governing equations for scaling of the flow field, droplet trajectories, and ice accretion on a rotating blade model. It derives a set of non-dimensional groups which govern the flow parameters for a rotating blade, including the Strouhal number, Froude number, drag coefficient of droplets and droplet based Reynolds number, droplet inertia parameter, and two other new parameters. The scaling methodology can also be utilized to determine alternative test conditions to predict rime ice conditions on a rotating blade. The study provides valuable insight to predict ice accretion on large wind turbine blade sections in the field based on scaled smaller blade sections tested in a laboratory setting.