Biconvex Airfoil Research Articles

Numerical Analysis of Aerodynamic and Shock Wave Characteristics of Biconvex and Double-Wedge Shape Airfoils for Supersonic Flow

This present study describes the aerodynamic characteristics of supersonic flow over biconvex and double wedge airfoils using a finite volume method-based commercial CFD code Ansys Fluent. A steady-state RANS approach is used with SST k-ω viscous modeling. A series of simulations are conducted to analyze the characteristics of shock and expansion waves formed around the airfoils for Mach numbers ranging from 1.4 to 3.4 with varying angles of attack (α) from 0° to 20°. It is observed that the lift and drag coefficients both increase with the angle of attack for a fixed Mach number and decrease with the Mach number for a fixed angle of attack. Double wedge airfoil generates about 5% more lift at a low Mach number and 1% more lift at a higher Mach number compared to the biconvex airfoil. However, the biconvex airfoil generates lesser drag than the double wedge airfoil. The maximum value of the pressure coefficient (Cp ) is found to be 1.7 for biconvex airfoil and 1.4 for double wedge airfoil. The maximum value of the lift-to-drag ratio for biconvex airfoil is 7.63, occurs at 1.4 Mach number and 3.46° angle of attack, whereas the value for double wedge airfoil is 5.19 at the same Mach number with 4.47° angle of attack, which suggest that biconvex airfoil has a higher lift-to-drag ratio and gives a better aerodynamics performance. The shock waves start to detach after an angle of attack of 5° and the shock wave is fully detached at a 15° angle of attack for biconvex airfoil for Mach number of 1.4. For the same Mach number, the double wedge airfoil, the shock wave starts to form the same as the biconvex airfoil but the waves are fully detached at a lower angle of attack of 10°. With the increasing Mach number, the shock waves remain attached to the airfoil.

Comparative study over double wedge and biconvex airfoils for laminar flow using CFD

This paper is mainly focused on Supersonic Laminar Flow at Mach 3 for biconvex and double wedge airfoils. The coefficient of lift (Cl), coefficient of drag (Cd), and coefficient of moment along the respective airfoils are being analysed. The geometry of these is generated using the Designmodeler of ANSYS. Further, meshing is also achieved by ANSYS with around 50000 nodes which is satisfactory for the current flow analysis. The total number of iterations being set for the particular simulation is 1000. This article covers the approach of the Kutta-Joukowski theorem, from which we know that flow circulation impacts the lift of the airfoil and how it changes for biconvex and double wedge airfoils. Decisively, this paper delivers provides pressure, heat transfer, and velocity distribution for both the airfoils. This paper gives a comparative study of both the double wedge and the biconvex airfoils at MACH 3, zero angle of attack. The study will be analysing both the airfoils in 3D as well as in 2D.

Efficient global optimization method via clustering/classification methods and exploration strategy

The objective of this research is to efficiently solve complicated high dimensional optimization problems by using machine learning technologies. Recently, major optimization targets have been changed to more complicated ones such as discontinuous and high dimensional optimization problems. It is necessary to solve the high-dimensional optimization problems to obtain an innovate design from topology design optimizations that have enormous numbers of design variables in order to express various topologies/shapes. In this research, therefore, an efficient global optimization method via clustering/classification methods and exploration strategy (EGOCCS) is developed to efficiently solve the high dimensional optimization problems without using probabilistic values as standard deviation, that are generally given/utilized in Gaussian process, and to reduce the construction cost of response surface models. Two optimization problems are solved to verify the usefulness of the developed method of EGOCCS. First optimization is executed to demonstrate the validity of the EGOCCS in 2, 10, 40, 80 and 160-dimensional analytic function problems that are also solved by the Bayesian optimization for comparison purposes. It is confirmed that the EGOCCS with radial basis function interpolation approach can obtain the best solutions in many analytic function problems with larger numbers of design variables. Second optimization is executed to examine the effect of the EGOCCS in high dimensional aerodynamic shape optimization problems for a two-dimensional biconvex airfoil that are also solved by a genetic algorithm for comparison purposes. It is confirmed that the EGOCCS can be efficiently used in the high dimensional aerodynamic shape optimization problems.

A CFD-Compatible Amplification Factor Transport Equation for Oblique Tollmien-Schlichting Waves in Supersonic Boundary Layers

Boundary layer transition is a hot research topic in fluid mechanics and aerospace engineering. In low-speed flows, two-dimensional Tollmien-Schlichting (T-S) waves always dominate the flow instability, which has been modeled by Coder and Maughmer from 2013. However, in supersonic flows, three-dimensional oblique Tollmien-Schlichting waves become dominant in flow instability. Inspired by Coder and Maughmer’s NTS amplification factor transport equation for two-dimensional Tollmien-Schlichting waves in low-speed flows and Kroo and Sturdza’s linear stability theory (LST) analysis results for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique Tollmien-Schlichting waves has been developed based on LST. The compressible Falkner-Skan similarity equations are introduced to build the relationships between nonlocal variables and local variables so that all the variables used in the present model can be calculated using local variables. Applications of this new transport equation to the flows over supersonic flat plate, 3% thick biconvex airfoil, and one modified supersonic laminar airfoil show promising results compared with the standard LST analysis results.

CFD analysis of the aerodynamic characteristics of biconvex airfoil at compressible and high Mach numbers flow

In the present study, numerical investigation of the turbulent flow over a biconvex airfoil at compressible and high Mach numbers flow is done using computational fluid dynamics (CFD). The flow is considered as turbulent, two-dimensional, steady and compressible. For this purpose, three Reynolds number of 2.4 × 107, 2.9 × 107 and 3.3 × 107 are considered. The simulations are implemented using the commercial software Ansys Fluent 16. The results are obtained with Reynolds-averaged Navier–Stokes (RANS), and for simulating the flow turbulence, SST k–ω turbulence model is carried out. The results show that the lift coefficient (CL) and drag coefficient (CD) increase by the increment of the angle of attack (α). The lift-to-drag ratio (CL/CD) is improved by increasing the Mach number (Ma) and cause to delay the boundary layer separation. Increasing the Mach number affects the stall angle which causes to increase it from α = 22° to α = 30° from Ma = 1 to Ma = 1.4.

Hydraulic analogy and visualisation of two-dimensional compressible fluid flows: part 2: water table experiments

In part 1, the theoretical aspects of hydraulic analogy are given in detail. In this part, the water table experiments are reported. Pictures of the flow patterns over different models show the formations of analogous shock waves and expansion fans. Pointed airfoils are tested first. Both biconvex and diamond airfoils are used. Busemann biplane model is included. The formation of a shock over a sharp pointed concave body is also tested. For blunt bodies, flow over a cylinder with a detached bow shock is studied. A sharp and not-so-sharp-spike added to the cylinder and the flow patterns are compared. Shocks inside and outside convergent-divergent nozzles are shown. Also, some results are reported for an experiment with a very simple arrangement of a plate in a plastic container, where the model is fixed, and the water is poured on the plate. Such an arrangement can be used for classroom demonstrations. Issues of manufacturing the models, nozzles and airfoils, are studied as well. Measurement techniques for obtaining quantitative results are briefly mentioned. Finally, concluding remarks about the educational use of this experiment are discussed.

Computation of transonic internal flow around a biconvex airfoil with cavity

At transonic flow conditions, unsteady self-excited shock waves are frequently observed in several modern internal aeronautical applications such as in turbine cascades, compressor blades, butterfly valves, fans, nozzles, diffusers and so on. The appearance of shock oscillation often causes serious problems such as aero-acoustic noise, non-synchronous vibration (NSV), intense drag rise, high cycle fatigue failure (HCF) and buffeting. In recent years, the effect of various passive means on the airfoil are investigated both experimentally and numerically to find the effectiveness as a shock control device. In the present study, the transonic internal flow around an airfoil using a cavity as a passive means of shock control was investigated numerically. Computational results are validated with available experimental data. Results showed that the airfoil with cavity significantly reduced the flow field unsteadiness such as the amplitude of pressure oscillation and root mean square of pressure oscillation.

Numerical and analytical solution of compressible flow over double wedge and biconvex airfoils

Purpose – The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).Design/methodology/approach – Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work....

Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows

The approach to determine pressure fields and integral loads from planar velocimetry data is discussed, in relation to the implementation for incompressible and compressible flows around two-dimensional objects. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure field from the experimental data, by making use of the flow constitutive equations. In this paper the implementation for two specific application areas is addressed. The first is time-mean pressure field and force evaluation from velocity ensemble statistics, as obtained from time-uncorrelated PIV acquisition, for incompressible flow. Two test cases are considered for this flow regime: the unsteady vortical flow around a square section cylinder at incidence, as well as the force characterization of a low-speed airfoil. The second topic considers the extension of the method to steady compressible flow, with the supersonic flow around a bi-convex airfoil as experimental test case. As in this flow regime the density appears as an extra unknown in the momentum equation, additional flow equations need to be invoked. A convenient approach for this was found, using the gas law and the adiabatic flow condition, with which the pressure-integration procedure becomes essentially the same as for the incompressible case.

ANALYSIS OF A MESHFREE METHOD FOR THE COMPRESSIBLE EULER EQUATIONS

Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

Small-Scale Roughness Effects on Laminar Separation

In this study an interacting boundary-layer (IBL) algorithm is used to investigate small-scale surface roughness effects on the laminar separation mechanism, where “small-scale” is intended to mean roughness fully contained within the boundary layer. Steady, laminar breakaway separation is computed for two-dimensional flow past a symmetric biconvex airfoil with small-scale roughness elements added to the surface. In this case the flow separation is generated at the trailing edge of a biconvex airfoil, but results are relevant to laminar separation points in general such as that occurring in the leading-edge region. The study is interested primarily in the laminar separation point, and not necessarily the entire bubble and downstream region. The use of the IBL method made it possible to achieve the required fine resolution in areas of interest. For some roughness geometries and flow conditions, up to 15000 grid points (over 4 million total grid points) were used in the streamwise direction to capture the resulting flow physics, which would still be time restrictive with a full Navier–Stokes algorithm. A number of different small-scale roughness configurations were evaluated including variations of roughness height, wavelength, distribution, and geometry. Results from this work show that small-scale roughness can alter the characteristics of the laminar separation point in low-speed flows.

A comparison of time integration methods in an unsteady low‐Reynolds‐number flow

AbstractThis paper describes three different time integration methods for unsteady incompressible Navier–Stokes equations. Explicit Euler and fractional‐step Adams–Bashford methods are compared with an implicit three‐level method based on a steady‐state SIMPLE method. The implicit solver employs a dual time stepping and an iteration within the time step. The spatial discretization is based on a co‐located finite‐volume technique. The influence of the convergence limits and the time‐step size on the accuracy of the predictions are studied. The efficiency of the different solvers is compared in a vortex‐shedding flow over a cylinder in the Reynolds number range of 100–1600. A high‐Reynolds‐number flow over a biconvex airfoil profile is also computed. The computations are performed in two dimensions. At the low‐Reynolds‐number range the explicit methods appear to be faster by a factor from 5 to 10. In the high‐Reynolds‐number case, the explicit Adams–Bashford method and the implicit method appear to be approximately equally fast while yielding similar results. Copyright © 2002 John Wiley & Sons, Ltd.

Studies on Alleviation of Buffet in Periodic Transonic Flow

We present some of the results of a transonic computational fluid dynamics (CFD) study performed on a biconvex airfoil with a splitter plate extension or with surface cooling with a view to suppress the periodic motion

Effect of Wind Tunnel Acoustic Modes on Linear Oscillating Cascade Aerodynamics

The aerodynamics of a biconvex airfoil cascade oscillating in torsion is investigated using the unsteady aerodynamic influence coefficient technique. For subsonic flow and reduced frequencies as large as 0.9, airfoil surface unsteady pressures resulting from oscillation of one of the airfoils are measured using flush-mounted high-frequency-response pressure transducers. The influence coefficient data are examined in detail and then used to predict the unsteady aerodynamics of a cascade oscillating at various interblade phase angles. These results are correlated with experimental data obtained in the traveling-wave mode of oscillation and linearized analysis predictions. It is found that the unsteady pressure disturbances created by an oscillating airfoil excite wind tunnel acoustic modes, which have detrimental effects on the experimental results. Acoustic treatment is proposed to rectify this problem.

Numerical study of the flow establishment time in hypersonic shock tunnels

This paper presents a numerical study of unsteady hypersonic viscous flows in 2D hypersonic shock tunnels. The numerical experiments on the combined nozzle/model flows, utilizing the configurations mounted in the test section of a 14.7-long shock tunnel, which has a design Mach number of Me = 6 and a stagnation temperature of T(0) = 3063 R, have been performed by solving the 2D Navier-Stokes equations with an ADI-type TVD scheme. The flow establishment times around aerodynamic models, such as a flat plate, a biconvex airfoil, thin and thick double wedges, and a circular cylinder, are calculated and compared. The analysis shows that, for the most severely separated case of a circular cylinder, the flow becomes stabilized within about 8 msec including the starting process, and its nondimensional flow establishment time is 46. The flow establishment time increases with increasing length of the separated region and decreases with increasing freestream velocity.

Wind Tunnel Wall Effects in a Linear Oscillating Cascade

Experiments in a linear oscillating cascade reveal that the wind tunnel walls enclosing the airfoils have, in some cases, a detrimental effect on the oscillating cascade aerodynamics. In a subsonic flow field, biconvex airfoils are driven simultaneously in harmonic, torsion-mode oscillations for a range of interblade phase angle values. It is found that the cascade dynamic periodicity—the airfoil-to-airfoil variation in unsteady surface pressure—is good for some values of interblade phase angle but poor for others. Correlation of the unsteady pressure data with oscillating flat plate cascade predictions is generally good for conditions where the periodicity is good and poor where the periodicity is poor. Calculations based upon linearized unsteady aerodynamic theory indicate that pressure waves reflected from the wind tunnel walls are responsible for the cases where there is poor periodicity and poor correlation with the predictions.

Effect of model cooling on periodic transonic flow

Experimental investigations were conducted in a small transonic intermittent tunnel on 14 and 18% thick biconvex airfoils to study the effect of model temperature on periodic transonic flows. The Reynolds number based on the model chord was in the range 0.7-0.9 x 106. Tests were conducted in the Mach number range of 0.7-0.85, and the model-to-tunnel stagnation temperature ratio range of 0.6-1.0. The models were cooled in liquid nitrogen to the required temperature before a run. The measurements included model surface mean pressure and temperatures and tunnel side wall dynamic pressures. The results showed a large effect of model temperature on mean pressure distribution and periodic buffet excitation levels. The effects observed are thought to correspond with what would happen to adiabatic flows at greatly increased Reynolds numbers. Nomenclature Cp = pressure coefficient Cpte = pressure coefficient measured at x/c =0.95 c = model chord length, mm / = frequency, Hz M = freestream Mach number MI = Mach number just upstream of the shock n = nondimensional frequency parameter, 2irfc/u p = rms pressure fluctuations, N/M2 q = kinetic pressure, N/M2 Re = Reynolds number based on model chord TW, Tad = wall and adiabatic recovery temperature, K / = times, s u - freestream velocity, m/s x,y = coordinates from the leading edge of model 5 = boundary-layer thickness

On the Application of a Linearized Unsteady Potential-Flow Analysis to Fan-Tip Cascades

A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the unsteady response to prescribed blade motions, has been applied to five two-dimensional cascade configurations. These include a flat-plate cascade and three cascades which are representative of the tip sections of current fan designs. Here the blades are closely spaced, highly staggered, and operate at low mean incidence. The fifth configuration is a NASA Lewis cascade of symmetric biconvex airfoils for which experimental measurements are available. Numerical solutions are presented that clearly illustrate the effects and importance of blade geometry and mean blade loading on the linearized unsteady response at high subsonic inlet Mach number and high blade-vibrational frequency. In addition, a good qualitative agreement is shown between the analytical predictions and experimental measurements for the cascade of symmetric biconvex airfoils. Finally, recommendations on the research needed to extend the range of application of linearized unsteady aerodynamic analyses are provided.

Unsteady Pressure Measurements on a Biconvex Airfoil in a Transonic Oscillating Cascade

Flush-mounted dynamic pressure transducers were installed on the center airfoil of a transonic oscillating cascade to measure the unsteady aerodynamic response as nine airfoils were simultaneously driven to provide 1.2 deg of pitching motion about the midchord. Initial tests were performed at an incidence angle of 0.0 deg and a Mach number of 0.65 in order to obtain results in a shock-free compressible flow field. Subsequent tests were performed at an angle of attack of 7.0 deg and a Mach number of 0.80 in order to observe the surface pressure response with an oscillating shock near the leading edge of the airfoil. Results are presented for interblade phase angles of 90 and −90 deg and at blade oscillatory frequencies of 200 and 500 Hz (semichord reduced frequencies up to about 0.5 at a Mach number of 0.80). Results from the zero-incidence cascade are compared with a classical unsteady flat-plate analysis. Flow visualization results depicting the shock motion on the airfoils in the high-incidence cascade are discussed. The airfoil pressure data are tabulated.

Relative effects of Reynolds number and freestream turbulence in transonic flow

Present herein are the experimental results on the effect of freestream turbulence in the range 0.34% < TuQO<3.6% on the pressure distribution over an 18%-thick biconvex airfoil with and without leadingedge trips for a condition corresponding to a significant shock-induced separation. The results are compared with similar measurements on a wall-mounted bump model with a thicker boundary layer at the foot of the shock. The results showed that at low Reynolds numbers the effect of freestream turbulence is primarily through the change in the boundary-layer transition. However, the freestream turbulence had a strong effect on the pressure distribution downstream of the shock interaction at a higher Reynolds number.