Inverse Design Code Research Articles

DLR transonic inverse design code, extensions and modifications to increase versatility and robustness

ABSTRACTThe DLR inverse design code computes the wing geometry for a prescribed target pressure distribution. It is based on the numerical solution of the integral inverse transonic small perturbation (TSP) equations. In this work, several extensions and modifications of the inverse design code are described. Results are validated with corresponding redesign test cases. The first modification concerns applications for high transonic Mach numbers or cases with strong shocks. The introduced modifications enable converged design solutions for cases where the original method failed. The second modification is the extension of the code to general non-planar wings. Previously, the design code was restricted to non-planar wing designs with small dihedral or to nacelle design. A third modification concerns aerofoil/wings designed for wind-tunnel design. In order to design a swept wing between two wind-tunnel walls, the solution method was extended to two symmetry planes. The introduced extensions and modifications have increased the robustness and range of applicability of the inverse design code.

Inverse design of horizontal axis wind turbine blades using a vortex line method

AbstractA new inverse design process for horizontal axis wind turbine blades is developed to account for three‐dimensional blade features such as non‐planar wing tip. The multidimensional Newton iteration method combined with a vortex line method is used to provide blade geometry parameters given desired aerodynamic behaviors such as lift coefficient and axial induction. The Jacobian matrix is visualized to show the effect of the change of the blade twist and chord on the change of the aerodynamic behaviors. The method is validated for a canonical straight blade with uniform lift coefficient and axial induction distributions. The results show an excellent agreement with those obtained by PROPID, which is a blade element momentum theory‐based inverse design code. The National Renewable Energy Laboratory Phase VI blade is used to validate the method for a straight blade with non‐uniform distributions of the lift coefficient and axial induction. The method is also applied successfully to a non‐straight blade design with a non‐planar wing tip. A noticeable change in the twist and chord for this non‐straight blade is seen compared with a straight blade. Finally, the inverse design code is used to make a large rotor blade, and the power output generated by this blade is computed. Copyright © 2014 John Wiley & Sons, Ltd.

Inverse Design of 3D Multistage Transonic Fans at Dual Operating Points

Semi-inverse design is the automatic recambering of an aerofoil during a computational fluid dynamics (CFD) calculation in order to achieve a target lift distribution while maintaining thickness, hence, “semi-inverse.” In this design method, the streamwise distribution of curvature is replaced by a streamwise distribution of lift. The authors have developed an inverse design code based on the method of Hield (2008, “Semi-Inverse Design Applied to an Eight Stage Transonic Axial Flow Compressor,” ASME Paper No. GT2008-50430), which can rapidly design three-dimensional fan blades in a multistage environment. The algorithm uses an inner loop to design to radially varying target lift distributions, an outer loop to achieve radial distributions of stage pressure ratio and exit flow angle, and a choked nozzle to set design mass flow. The code is easily wrapped around any CFD solver. In this paper, we describe a novel algorithm for designing simultaneously for specified performance at full speed and peak efficiency at part speed, without trade-offs between the targets at each of the two operating points. We also introduce a novel adaptive target lift distribution, which automatically develops discontinuous changes of calculated magnitude, based on the passage shock, eliminating erroneous lift demands in the shock vicinity and maintaining a smooth aerofoil.

An evaluation testbed for wind turbine blade tip designs-baseline case

SUMMARY A 3.3 m diameter wind turbine rotor has been designed, fabricated, and tested in a large scale university operated indoor wind facility. The rotor was custom designed for operation in the wind facility and allowed for exchangeable blade tips such that various tip designs can be tested for their effects on performance. The design of the rotor blades utilized the NREL S83X series airfoils, which were blended along the blade. Two-dimensional airfoil performance data were utilized, where available, with models used for post stall performance. The inverse design code PROPID, using Blade Element Momentum (BEM) theory was utilized for the blade design and blade performance was predicted. Subsequently, blades were fabricated in the conventional manner using glass fiber hand laid in computer numerical control (CNC) machined molds. Turbine power production measurements were completed covering a range of mean wind speeds, 3.6 m/s to 11 m/s nominal, and turbine rotor shaft rotational rates, 100 rpm to 240 rpm. This testing allowed the total power produced by the blades to be determined as a function of input wind speed, as traditionally found in power curves for commercial turbines. The coefficient of power, CP, was determined as a function of the tip speed ratio λ and peak CP was found to approach 0.42 at the design λ of 6.7. At the design shaft speed of 200 rpm, the maximum power produced was 1.45 kW at 11 m/s. Experimental results were compared with model predictions. The model predicted the performance fairly accurately for λ > 6.5, whereas the model underpredicted performance at high wind speeds and was less successful at predicting CP accurately at low λ. Copyright © 2011 John Wiley & Sons, Ltd.

Design of axial fan using inverse design method

The axial fans for cooling condensers were designed by inverse design code TURBOdesign-1. The parameters of the inverse design were set by DOE (design of experiments). By changing the design parameters, such as the distribution of the blade loading, spanwise circulation distribution and stacking, 32 different fan designs were created for the screening of parameters. The overall performance and the local flow field of these fans were computed using a commercial CFD code. The results of the CFD computations were analyzed by DOE. The pressure rise and efficiency were selected as the main responses, and the main effects of the design parameters on the responses were discussed. The main design parameters for the optimum design of the fan were decided from the results of the screening procedure. We designed the optimum axial fan by RSM (response surface method). The design center fan was made by RP (rapid prototype) and the performance was tested using a fan tester based on AMCA standards. These procedures ensured proper screening of parameters and optimum design of the axial fan.

Inverse Design of Adaptive Airfoils with Aircraft Performance Considerations

Recent advances in the development of inverse airfoil design methods now allow for the incorporation of aircraft performance considerations in the design of a non-flapped airfoil. While these improvements make airfoil-aircraft matching considerably easier, there is a need for a similar capability for adaptive airfoils. This paper presents a design formulation that incorporates aircraft performance considerations in the inverse design of low-speed laminar-flow adaptive airfoils. The benefit of using adaptive airfoils is that the size of the low-drag region of the drag polar can be effectively increased without increasing the thickness of the airfoil. Two aircraft performance parameters are considered: level-flight maximum speed and maximum range. It is shown that the lift coefficient for the lower and upper corners of the airfoil low-drag range can be appropriately adjusted to tailor the airfoil for these two aircraft performance parameters. The design problem is posed as a part of a multidimensional Newton iteration in an existing conformal-mapping based inverse design code, PROFOIL. This formulation automatically adjusts the lift coefficients for the corners of the low-drag range for a given flap deflection as required for the airfoil-aircraft matching. Examples are presented to illustrate the benefits of the process for a general aviation aircraft and the results are validated by comparison with results from post-design aircraft performance computations.

Incorporation of Aircraft Performance Considerations in Inverse Airfoil Design

Although significant advances have been made in inverse airfoil design methodology, the tailoring of an airfoil to maximize one or more aircraft performance parameters still involves cycling between airfoil design and aircraft performance computations. A design formulation is presented that incorporates aircraft performance considerations in the inverse design of low-speed laminar-flow airfoils for piston engine driven propeller-powered airplanes. Two aircraft performance parameters are considered: level-flight maximum speed and maximum range. It is shown that the lift coefficient for the lower and upper corners of the airfoil low-drag range can be appropriately adjusted to tailor the airfoil for these two aircraft performance parameters. The design problem is posed as a part of a multidimensional Newton iteration in an existing conformal-mapping based inverse design code, PROFOIL. This formulation automatically adjusts the lift coefficients for the corners of the low-drag range as required for the airfoil‐aircraft matching. The design formulation also has the capability to handle a constraint on the stall speed by automatically adjusting the wing area to account for changes to the airfoil maximum lift coefficient. Two examples are presented to illustrate the process for a general aviation aircraft, and the results are validated by comparison with results from postdesign aircraft performance computations. Nomenclature A R= wing aspect ratio b = wing span C D = aircraft or wing drag coefficient based on Sw Cd = airfoil drag coefficient based on chord CL = aircraft or wing lift coefficient based on Sw Cl = airfoil lift coefficient based on chord

Inverse Design of Centrifugal Compressor Stages Using a Meanline Approach

This article discusses an approach for determining meanline geometric parameters of centrifugal compressor stages given specified performance requirements. This is commonly known as the inverse design approach. The opposite process, that of calculating performance parameters based on geometry input is usually called analysis, or direct calculation. An algorithm and computer code implementing the inverse approach is described. As an alternative to commercially available inverse design codes, this tool is intended for exclusive OEM use and calls a trusted database of loss models for individual stage components, such as impellers, guide vanes, diffusers, etc. The algorithm extends applicability of the inverse design code by ensuring energy conservation for any working medium, like imperfect gases. The concept of loss coefficient for rotating impellers is introduced for improved loss modelling. The governing conservation equations for each component of a stage are presented, and then described in terms of an iterative procedure which calculates the required one‐dimensional geometry. A graphical user interface which facilitates user input and presentation of results is discussed briefly. The object‐oriented nature of the code is highlighted as a platform which easily provides for maintainability and future extensions.

Investigation of an Inversely Designed Centrifugal Compressor Stage—Part I: Design and Numerical Verification

In this paper the three-dimensional inverse design code TURBOdesign-1 is applied to the design of the blade geometry of a centrifugal compressor impeller with splitter blades. In the design of conventional impellers the splitter blades normally have the same geometry as the full blades and are placed at mid-pitch location between the two full blades, which can usually result in a mismatch between the flow angle and blade angles at the splitter leading edge. In the inverse design method the splitter and full blade geometry is computed independently for a specified distribution of blade loading on the splitter and full blades. In this paper the basic design methodology is outlined and then the flow in the conventional and inverse designed impeller is compared in detail by using computational fluid dynamics (CFD) code TASCflow. The CFD results confirm that the inverse design impeller has a more uniform exit flow, better control of tip leakage flow and higher efficiency than the conventional impeller. The results also show that the shape of the trailing edge geometry has a very appreciable effect on the impeller Euler head and this must be accurately modeled in all CFD computations to ensure closer match between CFD and experimental results. Detailed measurements are presented in part II of the paper.

Aerodynamic Design of Transonic Wings Using the Target Pressure Optimization Approach

A design study of transonic wings has been performed by the hybrid inverse optimization method. An existing target pressure optimization code for the transonic airfoil inverse design has been extended to obtain a target pressure distribution for transonic wing design. The shock strength was minimized and the isobar line sweep angle on the upper surface of the wing was maximized to obtain minimum compressibility drag. With the target pressure at each design section, an inverse design code was run to obtain a subsequent wing geometry. The designed wing showed better performance than the baseline wing at the given design condition, and geometric constraints on the section contour area were successfully satisfied. Design result showed that the inverse design using the target pressure optimization approach is very efficient in obtaining a transonic wing of high performance at a given design condition. However, single-point designs do not guarantee off-design performance. Multi-point design is needed to obtain a transonic wing of high performance at broader range of flow conditions.

Genetic optimization of target pressure distributions for inverse design methods

A genetic algorithm has been applied to optimize target pressure distributions for inverse design methods. Pressure distributions around airfoils are parameterized by B-spline polygons, and the airfoil drag is minimized under constraints on lift, airfoil thickness, and other design principles. Once target pressure distributions are obtained, corresponding airfoil/wing geometries can be computed by an inverse design code coupled with a Navier-Stokes solver. Successful design results were obtained for transonic cases with and without a shock wave.

Inverse design of super-elliptic cooling passages in coated turbine blade airfoils

A highly accurate and reliable algorithm capable of performing automatic inverse design of coolant flow passage numbers, shapes, sizes, and locations inside coated solid objects has been developed. The user has the freedom to specify arbitrary temperatures and heat fluxes at the points on the outer surface of the object, and either temperatures or heat fluxes on the surfaces of the yet unknown coolant flow passages. The number of passages required could be guessed and the algorithm will automatically eliminate the unnecessary passages. The method allows even inexperienced designers to achieve an optimal configuration of coolant passages in a single computer run while satisfying user-specified manufacturing constraints that were incorporated via a barrier function method. The optimization algorithms used in this inverse design code were based on gradient search and on a modified Newton search. A simple method for escaping from local minima has been implemented that involves switching between two different formulations of the objective function. The optimal value of the gradient search parameter was found using a simple method of fitting a highly accurate spline through a set of points in the cost function/search parameter plane, and seeking out the value that will generate minimal error.

Design and Performance of a Fixed, Nonaccelerating Guide Vane Cascade That Operates Over an Inlet Flow Angle Range of 60 Deg

A unique set of wind tunnel guide vanes are designed with an inverse design code and analyzed with a panel method and an integral boundary layer code developed at the NASA Lewis Research Center. The fixed guide vanes, 80 ft long with 6-ft chord length, were designed for the NASA Ames 40 × 80/80 × 120 ft Wind Tunnel. Low subsonic flow is accepted over a 60 deg range of inlet angle from either the 40 × 80 leg or the 80 × 120 leg of the wind tunnel, and directed axially into the main leg of the tunnel where drive fans are located. Experimental tests of 1/10-scale models were conducted to verify design calculations.