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The aim of this paper is to demonstrate the effects of the shape optimization on the missile performance at supersonic speeds. The N1G missile model shape variation, which decreased its aerodynamic drag and increased its aerodynamic lift at supersonic flow under determined constraints, was numerically investigated. Missile geometry was selected fro...
Citations
... The numerical part of the study has been carried out with the software ANSYS coupled with CFD. In [11] a MOGA algorithm is used to optimize the aerodynamic shape of a missile. The numerical investigation of the aerodynamic coefficients, specifically drag and lift, was done using CFD analysis with Ansys Fluent software. ...
... In our work the integration of this software with the CFD method enabled the generation of drag and lift coefficients, as well as the characterization of the flow field around the selected profile [11] [15]. ...
The design of wind turbine's blades significantly
impacts the aerodynamic performance and the overall efficiency
of a horizontal axis wind turbine. In this paper, ANSYS
simulation is used to examine the aerodynamic properties of the
NACA 2412 airfoil. The NACA 2412 profile is widely used in
different wind energy due to its favorable aerodynamic
characteristics and performance qualities. This study examines
aerodynamic parameters such as lift and drag for a range of
angles of attack. The simulations aim to provide information on
the behavior of the aerodynamic profile using ANSYS coupled
with CFD methods, which will lead to a better understanding of
its performance and contribute to the optimization of wind
turbine design.
... The study has been conducted at supersonic speeds. The result of this study is that optimization can increase the lift-to-drag ratio by 11-17% at supersonic speeds [9]. ...
... The grid convergence index for a fine mesh to the medium can be seen from Equation (8). The ratio between the medium and coarse grid can be calculated by Equation (9). The relative error value can generally be written as Equation (10). ...
... Menter et al. [20] determined the polar curve of an aircraft by numerical simulation. The results were successfully validated with experimental data.Şumnu et al. [21] demonstrated the effects of shape optimization on the missile performance at supersonic speeds. The aerodynamic coefficients of drag and lift under different Mach numbers and different angles of attack were investigated numerically by means of CFD ANSYS Fluent software. ...
Vertical take-off and landing (VTOL) aircraft have become important aerial vehicles for various sectors, such as security, health, and commercial sectors. These vehicles are capable of operating in different flight modes, allowing for the covering of most flight requirements in most environments. A tail-sitter aircraft is a type of VTOL vehicle that has the ability to take off and land vertically on it elevators (its tail) or on some rigid support element that extends behind the trailing edge. Most of the tail-sitter aircraft are designed with a fixed-wing adaptation rather than having their own design. The design of the tail-sitter carried out in this work had the particularity of not being an adaptation of a quad-rotor system in a commercial swept-wing aircraft, but, rather, was made from its own geometry in a twin-rotor configuration. The design was performed using ANSYS SpaceClaim CAD software, and a numerical analysis of the performance was carried out in ANSYS Fluent CFD software. The numerical results were satisfactorily validated with empirical correlations for the calculation of the polar curve, and the performance of the proposed tail-sitter was satisfactory compared to those found in the literature. The results of velocity and pressure contours were obtained for various angles of attack. The force and moment coefficients obtained showed trends similar to those reported in the literature.
... Their experimental data demonstrated the reliable condition for optimized shape design of rotor airfoil. Among many approaches, one of the effective algorithms that have been utilized by researchers for aerodynamics shape design is Genetic Algorithms (Chan et al. 2018;Daróczy et al. 2018;Darwish, et al. 2018;Ebrahimi and Jahangirian 2017;Gao et al. 2017;Ghalandari et al. 2019;Liu et al. 2017;Qin et al. 2018;Saleem and Kim 2020;Şumnu et al. 2020;Wang and Zhao 2019;Yi et al. 2019). Chan et al. (2018) developed an optimization model based on the genetic algorithm to enhance the power coefficient of the Savonius wind turbine. ...
In the traditional methods, optimization and mesh generation in computational fluid dynamics are separate procedures, which increases the time and calculation effort. This issue has been addressed by a shape optimization approach based on the binary genetic algorithm coupled with the image-processing method for drag reduction purposes. A system-specified code in MATLAB software is developed to find the optimized configuration. Accurate filters in the image-processing method are used to detect the edge and corners of the imported obstacles in the flow field to generate suitable grids. A turbulent flow field over obstacles was modeled by Chien’s low-Reynolds k − ε model and finite volume methods with stagger grids to solve governing equations. Combining the binary genetic algorithm with the image-processing method is an effective method to optimize shape configuration and mesh generation. The drag coefficients of the generated shapes are determined and the optimum one is obtained. A good agreement is obtained by comparing the obtained results with wind tunnel experimental data.
... The 3D compressible RANS equations are solved using the shear-stress transport (SST) renormalization group K-ω turbulence model. The SST K-ω model is adopted as it has been widely used in the numerical calculation of multiple flow problems, such as airfoil boundary layer [14], supersonic vehicle design [15], supersonic flow [16], and especially in aerodynamic shape optimization [17]. The second-order upwind scheme is used for the discretization of the convective terms in all transport equations. ...
In this study, the aerodynamic uncertainty analysis and optimization of a conventional axisymmetric vehicle with an aerodynamic configuration were investigated. The prediction precision of the typical aerodynamic performance estimating methods, namely, engineering estimation and numerical simulation, was compared using the wind tunnel test data of the vehicle. Then, using a modified missile data compendium (DATCOM) software, a high-efficiency and high-precision method was developed, which was applied to analyze and characterize the aerodynamic parameters of the axisymmetric vehicle. To enhance the robustness and reliability of aerodynamic performance, an uncertainty-based design optimization (UDO) framework was established. The design space was scaled by parameter sensitivity analysis, and improved computational efficiency was achieved by developing parallel polynomial chaos expansions (PCEs). The optimized results show that the modified method exhibits high accuracy in predicting aerodynamic performance. For the same constraints, the results of the deterministic design optimization (DDO) showed that compared with the initial scheme, the probability of the controllability-to-stability ratio satisfying the constraint decreased from 98.8% to 72.4%, and this value increased to 99.9% in the case of UDO. Compared with the results of the initial scheme and DDO, UDO achieved a considerable reduction in mean values and standard deviation of aerodynamic performances, which can ensure a higher probability of constraints meeting the design requirements, thereby, realizing a reliable and robust design.
... The maximum velocity (terminal velocity) near sea level without active propulsion, for a free fall from space or near space, could be estimated using a set of equations 17 and parameters of North Atlantic Treaty Organization (NATO) N1G missile model as described in [81]. Assuming a tungsten rod the parameters were set as follows: total mass 200 kg, diameter 10 cm (cross section area 78 cm 2 ) with a drag coefficient of 0.03, air medium density at sea level 1.5 kg/m 3 , and Earth's gravity 9.8 m/s 2 . ...
This Scientific Report documents an unclassified analysis and literature review of key aspects and challenges related to hypersonic missiles and hypervelocity projectiles. Specifically, it introduces the nature and evolution of hypersonic weapons, discusses current and future sensor systems capabilities for detecting
and tracking these missiles and projectiles, advance information fusion systems for developing timely course-of-actions, interception methods, and effector technologies to defeat hypersonic and hypervelocity threats. Other strategic aspects of hypersonic missiles and hypervelocity projectiles, such as cost and sustainment considerations, are examined and presented. Examples of concerning hypersonic missile scenarios, assuming paths initiated along Canada’s coastline, are provided for illustration purposes. The study aims to inform decision-making about the new threats of hypersonic missiles and to suggest potential research and development activities/initiatives to advance the Canadian Armed Forces' knowledge and expertise of hypersonic weapon capabilities.
... Pue et al. performed a multidisciplinary concept optimization of a ballistic missile [6]. Şumnu et al. used the Multi-objective Genetic Algorithm to optimize the aerodynamic shape of a missile in order to determine the optimum lift and drag coefficients [7]. ...
In this study, the feasibility of a new launcher concept that provides range extension for outdated ballistic munitions by speeding up them before their ignition is examined in detail. To analyze the efficiency of the new concept, multi-variable and single-variable optimization processes are conducted using the Multi-Objective Genetic Algorithm Method in the ModeFrontier environment. Launch angle, ejection velocity of the munition from the launcher, and ignition delay of the rocket motor after the ejection process are determined as design variables. An in-house MATLAB script is prepared and validated to perform numerical solutions of the munition’s two-dimensional trajectory. As a result of the optimization processes, graphical results are prepared to examine the effects of each design variable on munition’s range and to make a comparison between the flight trajectories of the munitions which are launched from classical and accelerator launchers. It is concluded that usage of the accelerator launcher concept provides approximately 20% range extension for the generic munition examined in this research when compared to the classical launcher. Since this new concept can easily be adapted to different types of outdated ballistic munitions and the cost of the accelerator launcher development process will probably less than the cost required to develop new munitions, it will be reasonable to develop accelerator launchers such as electromagnetic accelerators or catapult launchers in near future.
... In conclusion, the multifidelity model can obtain high-fidelity results with less cost. Multifidelity methods have been used in many fields, such as mechanism analysis, optimization design [29][30][31], statistical inference, and uncertainty quantification [32]. In the field of fluid dynamics, some scholars have applied the multifidelity method to flapping wing dynamics analysis [33,34], aerodynamic optimization [35][36][37][38], flight simulation [28,39,40], hypersonic aerodynamic load prediction [41], low-fidelity turbulence model correction [42,43], and uncertainty quantification of fluid dynamics system [44][45][46][47]. ...
A reduced order modeling method based on algorithm fusion and multifidelity framework for nonlinear unsteady aerodynamics is proposed to obtain a low-cost and high-precision unsteady aerodynamic model. This method integrates the traditional algorithm, intelligent algorithm, and multifidelity data fusion algorithm. In this method, the traditional algorithm is based on separated flow theory, the intelligent algorithm refers to the nonlinear autoregressive (NARX) method, and the multifidelity data fusion algorithm uses different fidelity data for aerodynamic modeling, which can shorten the time cost of data acquisition. In the process of modeling, firstly, a multifidelity model with NARX description provides a general intelligent algorithm framework for unsteady aerodynamics. Then, based on the separated flow theory, the correction equation from low-fidelity model to high-fidelity result is constructed, and the cuckoo algorithm based on chaos optimization is used to identify the parameters. In order to verify the effectiveness of the method, an unsteady aerodynamic model of NACA0012 airfoil is established. Three kinds of data with low, medium, and high fidelity are used for modeling. The low-fidelity and medium-fidelity data is obtained from the CFD-Euler solver and CFD-RANS solver, respectively, while the high-fidelity data comes from the experimental results. Then, the model is established, and its prediction of unsteady aerodynamic coefficients is in good agreement with the CFD results and the experimental data. After that, the model is applied to a two-dimensional aeroelastic system, and the bifurcation and limit cycle response analysis are compared with the experimental results, which further shows that the model can accurately capture the main flow characteristics in the flow range of low speed and high angle of attack. In addition, the convergence of the model is studied; the accuracy and generalization ability as well as applicability scope of the model are compared with other aerodynamic models and finally discussed.
1. Introduction
Most of the problems in aircraft aerodynamic design are closely related to unsteady aerodynamic forces. Aerodynamic modeling is a major foundation for flight overall parameter design, flight trajectory design, and flight maneuverability and stability analysis. The accuracy of the aerodynamic model directly affects the performance of the control system and the reliability of flight simulation [1]. There are many factors that can affect the aerodynamic force such as flight altitude, airspeed, movement form, and rudder interference, which leads to a strong nonlinear aerodynamic system. However, the traditional aerodynamic modeling method is based on the assumption of quasisteady and linearization theory, which cannot meet the requirements for advanced civil and military aircraft design. So, in recent years, unsteady and nonlinear aerodynamic modeling methods have been paid more and more attention. There are two major problems in the unsteady aerodynamic modeling, one is the calculation of dynamic derivative, and the other is the aerodynamic modeling at a high angle of attack. As the former directly determines flight quality analysis and flight control system design, the latter is one of the important ways to evaluate the performance of aircraft at a high angle of attack. Therefore, it is of great value to study the flight dynamic derivative identification methods as well as nonlinear and unsteady aerodynamic modeling at high angles of attack.
The unsteady aerodynamic modeling method appeared at the beginning of the 20th century, and a variety of modeling methods had been widely developed since the 1980s. These methods can be divided into two categories: traditional mathematical expression method and intelligent learning methods. The traditional mathematical expression methods are a kind of method which obtain mathematical relationships between aerodynamic force, flight states, control inputs, and other parameters according to the physical characteristics and statistical laws of aerodynamic force. The traditional aerodynamic model is based on a dynamic stability derivative at the beginning, which is used to predict the change of flight load after the flight parameters change. These kinds of models regard each dynamic stability derivative as a constant value independent of time and other variables, so these models are linear aerodynamic models and are only applicable to the linear flight states with a small angle of attack [2]. In order to expand the application range of these models, the nonlinear algebraic model [3], Fourier series model [4–6], integral equation model [7], state space model [8, 9], etc., were developed. However, generally speaking, the traditional mathematical expression method of aerodynamic modeling is more suitable for aerodynamic modeling with limited flight state range changes, such as the linear/steady aerodynamic modeling under certain altitude, speed, angle of attack, and other conditions. The relationship between aerodynamic force and flight height, velocity, angle of attack, sideslip angle, angular velocity, rudder angle, and other parameters is highly nonlinear for the aircraft with large changes in airspace, airspeed, flight attitude, and control surface deflection range. It is difficult for traditional mathematical modeling methods to give an accurate description of all the relationships with acceptable errors.
With the rapid development of computer technology and the integration of interdisciplinary ideas, many other mathematical methods have also been introduced into the field of unsteady aerodynamic modeling, such as the autoregressive model [10–12], Volterra series model [13–15], fuzzy logic method [16], neural network method [17–21], and support vector machine method [22–24], collectively referred to as the intelligent algorithm. The unsteady aerodynamic model based on these algorithms does not pay attention to the physical principles; that is to say, the relationship between the aerodynamic force and the input state quantity is regarded as a “black box.” The aerodynamic model is established by a large number of high-quality sample data, so this kind of model is also called the data-driven model.
Although these methods can give accurate prediction within the range of sample flight states, the ability of extrapolation is usually very poor. At present, the research of aerodynamic modeling based on the intelligent algorithm is mostly based on the results of the wind tunnel dynamic test or CFD calculation. However, the model based on wind tunnel and flight test is difficult to reflect the aerodynamic characteristics of all the flight states or motion forms we are interested in, and the high-fidelity CFD calculation may take a lot of time to obtain enough data, so it is difficult to directly use these aerodynamic models in flight simulation. In addition, when the parameters in the aerodynamic system increase, the number of sample flight states and the calculation requirement for modeling also increase, which makes many parameters cannot be identified. Compared with the traditional methods, these intelligent algorithm models are based on “sample data” and do not care about the flow characteristics, so they do not have a physical background and cannot provide more information for the subsequent application. Therefore, it is necessary to improve the intelligent algorithm to make it suitable for practical application.
To sum up, the aerodynamic model based on the traditional mathematical method needs full understanding of the flow characteristics. The stability of the model can meet the requirements, but the modeling process is very complex. Although the aerodynamic model based on the intelligent algorithm does not rely on physical equations, the generalization ability of the intelligent model is often unsatisfactory. Both of the two methods have their own shortcomings, which makes them difficult to be applied to engineering practice.
To solve this problem, this paper proposes a reduced order model (ROM) for unsteady aerodynamics, which combines the intelligent algorithm with a traditional mathematical model and can consider the aerodynamic nonlinearity at a high angle of attack. Specifically, the intelligent algorithm based on NARX is used to build the structure of nonlinear unsteady aerodynamic ROM. Then, the correction functions based on the aerodynamic physical characteristic assumption of the modified Leishman-Beddoes dynamic stall (LB for short) model [25] are added into the intelligent model, and the parameters of the correction functions are identified by aerodynamic data and intelligent algorithm. Finally, the nonlinear aerodynamic ROM is obtained.
For most of the existing data-driven aerodynamic ROM, the dataset comes from the same data source: numerical simulation, experiment, or flight testing. However, aerodynamic data often comes from different sources in practice, and the cost and accuracy are also different. In order to handle the balance between model accuracy and data generation cost, data-driven modeling driven by data fusion is receiving more and more attention [26]. Here, data fusion refers to the process of combining data and information from multiple sources in order to refine, estimate, and get a better understanding of the data [27], and data-driven modeling based on data fusion mainly refers to the multifidelity modeling method based on aerodynamic data with different fidelity. For aerodynamic data, generally, high-fidelity aerodynamic data are obtained through the flight test, wind tunnel test, or direct numerical simulation, while low-fidelity data usually comes from numerical simulation and simplified, such as rough discretization, relaxation convergence tolerance, low precision, and omission of physics [28]. For data with different fidelity, the cost of data acquisition becomes higher with the increase of data fidelity, and due to the limitation of cost, the amount of available data decreases with the increase of fidelity. In addition, it is difficult for high-fidelity data to include all interesting information, which makes the aerodynamic modeling based on these data expensive and unsatisfactory. For example, most experimental data come from harmonic motion rather than random motion. That is because random motion is vulnerable to external noise interference, and the data quality of harmonic motion is better. However, the dynamic information contained in harmonic motion is limited. Based on the above problem, the multifidelity method has been developed and widely used, which provides a general framework for fusing data with different fidelity in the modeling process. The basic idea of the commonly used multifidelity framework is to use low-fidelity data or models (physically driven or data-driven) to provide the dynamic trend, while high-fidelity data is used to correct the model to better reproduce the high-fidelity results. In conclusion, the multifidelity model can obtain high-fidelity results with less cost.
Multifidelity methods have been used in many fields, such as mechanism analysis, optimization design [29–31], statistical inference, and uncertainty quantification [32]. In the field of fluid dynamics, some scholars have applied the multifidelity method to flapping wing dynamics analysis [33, 34], aerodynamic optimization [35–38], flight simulation [28, 39, 40], hypersonic aerodynamic load prediction [41], low-fidelity turbulence model correction [42, 43], and uncertainty quantification of fluid dynamics system [44–47]. It is worth noting that most of these studies focus on the evaluation of steady-state aerodynamics to achieve rapid simulation and optimization, while there are few studies on unsteady multifidelity aerodynamic modeling. Because the generation of unsteady aerodynamic data is much more expensive than steady aerodynamic data, it is particularly important to explore the effectiveness of the unsteady aerodynamic multifidelity method. Ghoreyshi et al. [48] firstly showed that using both Euler and RANS data for modeling can improve the prediction results of aerodynamic ROM, and the results are better than that of the model based on a single data source. High-fidelity, low-fidelity, and multifidelity ROM are built by the NARX framework. The multifidelity ROM is constructed by adding low-fidelity time delay prediction as additional inputs of high-fidelity ROM. After that, Kou and Zhang [49] took the cokriging concept as the underlying theory and systematically introduced the problem of unsteady aerodynamic data fusion modeling. They built the multifidelity aerodynamic ROM with improved stability of NACA0012 airfoil under transonic conditions by using the NARX framework. The correction term of the model is constructed by the multicore neural network. Euler and unsteady RANS solvers are used to provide low-fidelity and high-fidelity data, respectively. Results show that only three groups of high-fidelity training cases of harmonic motion are needed to establish a high-fidelity model and obtain high-fidelity results.
In this paper, in order to improve the modeling efficiency of the ROM, the multifidelity data fusion modeling method is also introduced, using a small amount of high-fidelity data and a large amount of low-fidelity data to build the high-fidelity model. Using data fusion modeling is aimed at improving the efficiency of data acquisition as the cost of high-fidelity data is usually pretty high, which can also improve the modeling efficiency at the same time. In this paper, three kinds of data with different fidelity are used for fusion modeling. The low-fidelity data is obtained by the CFD solver based on Euler. It should be noted that these low-fidelity data can also reflect the real situation under certain restrictions. That is to say, although it is low-fidelity data, it still meets the accuracy requirements. The medium-fidelity data is obtained by the CFD solver based on RANS. The high-fidelity data comes from the existing experimental data. For the modeling process, firstly, the low-fidelity aerodynamic ROM is established by using low-fidelity data. Then, the nonlinear correction function is constructed based on the flow separation principle [25] and is added to the low-fidelity ROM. After that, the parameters of the nonlinear correction function are preliminarily identified by using the medium-fidelity data and the intelligent parameter identification method. Finally, the high-fidelity data from experiments is used to optimize the correction parameters, and the final high-fidelity nonlinear aerodynamic ROM is obtained. In order to verify the proposed high-fidelity nonlinear aerodynamic ROM, the lift and moment coefficients of NACA0012 airfoil in pitching and plunging motion are predicted and compared with the experimental data and CFD-RANS results. Then, the high-fidelity ROM is applied to the two-dimensional aeroelastic system. After that, the convergence of the model is analyzed, and its performance is compared with the traditional modified LB model and the intelligent aerodynamic model based on the RBF neural network.
2. Multifidelity Framework for Nonlinear Unsteady Aerodynamic ROM Materials and Methods
In this part, the multifidelity framework for nonlinear unsteady aerodynamic ROM based on traditional and intelligent algorithm fusion is introduced. It can be divided into the following parts. First of all, it is necessary to select a suitable multifidelity modeling method to develop the relationship between the low-fidelity model and the high-fidelity model. Secondly, the low-fidelity model is established. Thirdly, correction functions are constructed for the difference between the high-fidelity model and the low-fidelity model, and the parameters are identified. Finally, the nonlinear unsteady multifidelity aerodynamic model suitable for a certain speed range and high angle of attack can be obtained.
2.1. Multifidelity Modeling Method
The multifidelity model, that is, the models with different fidelity and computational efficiency, is combined in a certain way, so that the new model can obtain the accuracy of the high-fidelity model with less computational cost. The low-fidelity model can be divided into three categories, including the simplified model, data fitting model, and projection-based model [32]. Here, we use the data fitting model which is also a kind of data-driven model. To combine the low-fidelity model and the high-fidelity model, the method based on correction is adopted; that is, the low-fidelity model is modified by the data generated by the high-fidelity model. Currently, the main correction methods can be briefly divided into three categories [50]: (1)Additive and multiplicative corrections:(2)Comprehensive corrections:(3)Space mapping (input correction):where is the high-fidelity model and is the low-fidelity model. represents the multiplicative corrector while represents the additive corrector. is the input vector.
In this paper, comprehensive corrections are used. However, there are some differences with the standard form. We divide the input factors into two categories according to their effects on the nonlinear response of the system: . We think represents the input factor which can cause strong nonlinearity of the system response, is also a part of input factors, but the nonlinear response of the system caused by is very small. According to the above assumption, we divide the high-fidelity model and the low-fidelity model into two parts, respectively: where and are the total response of the system calculated by the high-fidelity model and the low-fidelity model, respectively. and are the response of the system caused by , and and are the response of the system caused by . Superscripts 1 and 2 are identifiers without mathematical meaning which represent the response part caused by and , respectively.
Because the previous assumption that the nonlinear response of the system caused by is very small, we think that the main difference between the high-fidelity model and the low-fidelity model is the difference between and , so only this part needs to be modified. And there is little difference between and , so we regard . Then, the relationship between the high-fidelity model and the low-fidelity model can be written as the following equation: where the multiplicative corrector and the additive corrector are both time-varying functions, which can be identified from high-fidelity data.
2.2. Reduced Order Modeling Methodology
2.2.1. Nonlinear Autoregressive with Exogenous Input (NARX) Description
Considering the unsteady time delay effect of aerodynamic force, the nonlinear autoregressive model (NARX) modeling method with exogenous input for typical nonlinear dynamic systems is used [51, 52]. For MIMO discrete-time systems, the NARX model can be written as follows: where is the time scale, is the system output at time , and is the system input at time . NARX is aimed at establishing the nonlinear relationship between the outputs and the inputs at the current and several previous time steps.
In the current study, the nonlinear aerodynamic ROM for two-dimensional airfoil with pitching and plunging freedom at low speed and high angle of attack is modeled; the two-dimensional aeroelastic system is shown in Figure 1. In this case, . and represent the lift coefficient and pitching moment coefficient at time , respectively. , represents the pitching angle of airfoils, while represents the plunging displacement. Let , can be also written as .
... In order to obtain thrust and power coefficients, there are analytical, experimental or numerical methods applied in the literature. Today, as a numerical method, Computational Fluid Dynamics (CFD) applications come to the fore, which helps to obtain aerodynamic investigation results of complex geometries in a short time [7]. In the literature, there exist various studies including CFD investigation on multi-rotor UAV propeller aerodynamic performance parameters. ...
In this article, a numerical investigation was performed on a quadrotor unmanned aeroial vehicles (UAV) propeller to examine the effects of airspeed and rotational speed on thrust coefficient, which is one of the most important parameters on propeller aerodynamic performance. For that purpose, Computational Fluid Dynamics (CFD) analyses of an 11-inch propeller were carried out at different airspeeds and rotational speeds in vertical climbing flight conditions. In order to have the optimum number of mesh elements in the computational domain, mesh independence analyses were also conducted. In conclusion, the results of the analyses with the k-ω SST turbulence model were shown that increase in rotational speed was led to higher turbulent kinetic energy. Furthermore, higher rotational speeds also resulted in higher differences between numerical estimations and experimental data but were found to become more independent from airspeed.
... Seven control points and fourteen design variables are used to form a hybrid airfoil profile. Thus, the profile of hybrid airfoil has more degrees of freedom [20]. At first, the leading edge of the full-scale airfoil is taken as the hybrid airfoil's leading edge and connected with an arbitrary aft section. ...
The size of aircraft models that can be tested in icing wind tunnels is limited by the dimensions of the facilities in present; it is an effective method to replace the large model with a hybrid airfoil to carry out the experiment. A design method of multiple control points for hybrid airfoil based on the similarity of flow field in the leading edge of airfoil is proposed. Aiming at generating the full-scale flow field and ice accretion on the leading edge, multiobjective genetic optimization algorithm is used to design the hybrid airfoil under different conditions by combining the airfoil parameterization and solution of spatial constraint. Pressure tests of hybrid airfoils are carried out and compared with the leading edge pressure of the corresponding full-scale airfoils. The design and experimental results show that the pressure coefficient deviation between the hybrid airfoils designed and the corresponding full-scale airfoil in the 15% chord length range of the leading edge is within 4%. Finally, the vortex distribution and ice accretion process of the two airfoils were simulated by the unsteady Reynolds-averaged-Navier–Stokes (URANS) equations and multistep ice numerical method; it is shown that the hybrid airfoil can provide the same vortex distribution and ice accretion with the full-scale airfoil.
