Inverse Designing Airfoil Aerodynamics in Compressible Flow by Target Pressure Distribution

2020 ◽  
pp. 308-319
Author(s):  
Naser Tanabi ◽  
Ahmad Barari ◽  
Shidvash Vakilipour ◽  
Marcos S. G. Tsuzuki
Keyword(s):  
Pressure Distribution ◽  
Compressible Flow ◽  
Target Pressure

A Novel Two Dimensional Viscous Inverse Design Method for Turbomachinery Blading

2002 ◽  
Author(s):  
L. de Vito ◽  
R. A. Van den Braembussche ◽  
H. Deconinck
Keyword(s):  
Pressure Distribution ◽  
Design Method ◽  
Turbine Blades ◽  
Inverse Design ◽  
Navier Stokes ◽  
Particular Solution ◽  
Target Pressure ◽  
Inverse Design Method ◽  
Euler Solver ◽  
Stagger Angle

This paper presents a novel iterative viscous inverse method for turbomachinery blading design. It is made up of two steps: The first one consists of an analysis by means of a Navier-Stokes solver, the second one is an inverse design by means of an Euler solver. The inverse design resorts to the concept of permeable wall, and recycles the ingredients of Demeulenaere’s inviscid inverse design method that was proven fast and robust. The re-design of the LS89 turbine nozzle blade, starting from different arbitrary profiles at subsonic and transonic flow regimes, demonstrates the merits of this approach. The method may result in more than one blade profile that meets the objective, i.e. that produces the viscous target pressure distribution. To select one particular solution among all candidates, a target mass flow is enforced by adjusting the outlet static pressure. The resulting profiles are smooth (oscillation-free). The design of turbine blades with arbitrary pressure distribution at transonic and supersonic outflow illustrates the correct behavior of the method for a large range of applications. The approach is flexible because only the pitch chord ratio is fixed and no limitations are imposed on the stagger angle.

Three-Dimensional Inverse Method for Turbomachinery Blading Design

1998 ◽  
Vol 120 (2) ◽  
pp. 247-255 ◽  
Author(s):  
A. Demeulenaere ◽  
R. Van den Braembussche
Keyword(s):  
Pressure Distribution ◽  
Three Dimensional ◽  
Suction Side ◽  
Flow Angle ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Lean Angle ◽  
Outlet Flow ◽  
Target Pressure ◽  
Euler Solver

An iterative procedure for three-dimensional blade design is presented, in which the three-dimensional blade shape is modified using a physical algorithm, based on the transpiration model. The transpiration flux is computed by means of a modified Euler solver, in which the target pressure distribution is imposed along the blade surfaces. Only a small number of modifications is needed to obtain the final geometry. The method is based on a high-resolution three-dimensional Euler solver. An upwind biased evaluation of the advective fluxes allows for a very low numerical entropy generation, and sharp shock capturing. Non-reflecting boundary conditions are applied along the inlet/outlet boundaries. The capabilities of the method are illustrated by redesigning a transonic compressor rotor blade, to achieve, for the same mass flow and outlet flow angle, a shock-free deceleration along the suction side. The second example concerns the design of a low aspect ratio turbine blade, with a positive compound lean to reduce the intensity of the passage vortices. The final blade is designed for an optimized pressure distribution, taking into account the forces resulting from the blade lean angle.

Inverse Design of Airfoils Using Convolutional Neural Network and Deep Neural Network

2021 ◽  
Author(s):  
Amit Kumar ◽  
Nagabhushana Rao Vadlamani
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Convolutional Neural Network ◽  
Pressure Distribution ◽  
Mean Squared Error ◽  
Inverse Design ◽  
Batch Size ◽  
Squared Error ◽  
Order Of Magnitude ◽  
Target Pressure

Abstract In this paper, we compare the efficacy of two neural network based models: Convolutional Neural Network (CNN) and Deep Neural Networks (DNN) to inverse design the airfoil shapes. Given the pressure distribution over the airfoil in pictorial (for CNN) or numerical form (for DNN), the trained neural networks predict the airfoil shapes. During the training phase, the critical hyper-parameters of both the models, namely — learning rate, number of epochs and batch size, are tuned to reduce the mean squared error (MSE) and increase the prediction accuracy. The training parameters in DNN are an order of magnitude lower than that of CNN and hence the DNN model is found to be ≈ 7× faster than the CNN. In addition, the accuracy of DNN is also observed to be superior to that of CNN. After processing the raw airfoil shapes, the smoothed airfoils are shown to yield the target pressure distribution thereby validating the framework.

scholarly journals Three-Dimensional Inverse Method for Turbomachinery Blading Design

1996 ◽  
Author(s):  
Alain Demeulenaere ◽  
René Van den Braembussche
Keyword(s):  
Pressure Distribution ◽  
Three Dimensional ◽  
Suction Side ◽  
Flow Angle ◽  
Transonic Compressor ◽  
Lean Angle ◽  
Outlet Flow ◽  
Target Pressure ◽  
Euler Solver ◽  
Numerical Entropy

An iterative procedure for 3D blade design is presented. The three-dimensional blade shape is modified using a physical algorithm, based on the transpiration model. The transpiration flux is computed by means of a modified Euler solver, in which the target pressure distribution is imposed along the blade surfaces. Only a small number of modifications is needed to obtain the final geometry. The method is based on a high resolution three-dimensional Euler solver. An upwind biased evaluation of the advective fluxes allows for a very low numerical entropy generation, and sharp shock capturing. The method is first validated, by redesigning an existing geometry, starting from a different one. It is further used to redesign a transonic compressor blade, to achieve, for the same mass flow and outlet flow angle, a shock free deceleration along the suction side. The last example concerns the design of a low aspect ratio turbine blade, with a positive compound lean to reduce the intensity of the passage vortices. The final blade is designed for an optimized pressure distribution, taking into account the forces resulting from the blade lean angle.

Aerodynamic design of gas turbine engine intake duct

2016 ◽  
Vol 88 (5) ◽  
pp. 605-612 ◽  
Author(s):  
Bambang I. Soemarwoto ◽  
Okko J. Boelens ◽  
Toni Kanakis
Keyword(s):  
Pressure Distribution ◽  
Gas Turbine ◽  
Flow Separation ◽  
Gas Turbine Engine ◽  
Optimization Approach ◽  
Aerodynamic Design ◽  
Content Type ◽  
Turbine Engine ◽  
Compressor Inlet ◽  
Target Pressure

Purpose The purpose of this paper is to provide a design solution of an engine intake duct suitable for delivering air to the compressor of a gas turbine engine of a general aviation turboprop aircraft, where the initial duct shape suffers a problem of flow distortion due to flow separation at the compressor inlet. Design/methodology/approach Aerodynamic design uses a three-dimensional inverse-by-optimization approach where the deviation from a desirable target pressure distribution is minimized by means of the adjoint method. Findings By virtue of a minimization algorithm, the specified target pressure distribution does not necessarily have to be fully realizable to drive the initial pressure distribution towards one with a favourable pressure gradient. The resulting optimized engine intake duct features a deceleration region, in a diverging channel, followed by an acceleration region, in a contracting channel, inhibiting flow separation on the compressor inlet plane. Practical implications The flow separation at the compressor inlet has been eliminated allowing proper installation of the engine and flight testing of the aircraft. Originality/value Placement and shaping of the intake duct of a turboshaft and turboprop gas turbine engine is a common industrial problem which can be challenging when the available space is limited. The inverse-by-optimization approach based on a reduced flow model, i.e. inviscid flow based on the Euler equations, and a specification of a simple target pressure distribution constitutes an efficient method to overcome the challenge.

Rotordynamic Coefficients for Partially Tapered Annular Seals: Part II—Compressible Flow

1991 ◽  
Vol 113 (1) ◽  
pp. 53-57
Author(s):  
J. K. Scharrer ◽  
C. C. Nelson
Keyword(s):  
Pressure Distribution ◽  
Compressible Flow ◽  
Order Continuity ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Component Test ◽  
Annular Seal ◽  
Complex Differential Equations ◽  
Basic Equations

The basic equations are derived for compressible flow in an annular seal with a partially tapered clearance. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled by Moody’s equation for roughness. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are solved exactly, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are reduced to three ordinary, complex, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynamic coefficients. Since no component test data exist for this type of seal, the results of a parametric study on the effect of the taper length/seal length ratio on the seal leakage and rotordynamic coefficients are presented.

Some Aspects of Laminar Boundary Layer Separation in Compressible Flow with no Heat Transfer to the Wall

1953 ◽  
Vol 4 (2) ◽  
pp. 123-150 ◽  
Author(s):  
G. E. Gadd
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Distribution ◽  
Compressible Flow ◽  
Laminar Boundary Layer ◽  
Free Stream ◽  
Boundary Layer Separation ◽  
Absolute Temperature ◽  
Laminar Separation

SummaryAn analysis has been made which suggests that, with the types of pressure distribution most usual in practice and free stream Mach numbers up to 10, no serious errors would be introduced into the calculation of the laminar separation point by the assumption that σ, the Prandtl number, and ω, the index of variation of viscosity with absolute temperature, are equal to unity. (Typical actual values of σ and ω for air are 0.72 and 0.89 respectively).

A Novel Quasi-3D Design Method for Centrifugal Compressor Impeller on the Blade-to-Blade Plane

2011 ◽  
Author(s):  
Farzad Poursadegh ◽  
Ali Hajilouy-Benisi ◽  
Mahdi Nili-Ahmadabadi
Keyword(s):  
Pressure Distribution ◽  
Centrifugal Compressor ◽  
Design Method ◽  
Pressure Ratio ◽  
Design Procedure ◽  
Navier Stokes ◽  
3D Analysis ◽  
3D Design ◽  
Compressor Impeller ◽  
Target Pressure

In this research, a novel quasi-3D design method is developed for the centrifugal compressor impeller on the blade-to-blade plane. In this method, an iterative inverse design method called Ball-Spine Algorithm (BSA) is incorporated into the quasi-3D analysis code solving the Euler equations on the blade-to-blade and meridional planes at each shape modification step. In design procedure, the difference between the target and current pressure distribution along the suction or pressure sides of the impeller causes the blade-to-blade profile to be changed and the target pressure distribution to be satisfied. In order to validate the quasi-3D analysis code, the centrifugal compressor of a gas turbine is investigated numerically using a full 3D Navier-Stokes analysis code. The meridional and blade-to-blade planes pressure distributions obtained from quasi-3D and 3D analysis codes are compared showing good agreement between them. Furthermore, the pressure ratio and efficiency of the centrifugal compressor is obtained by some experiments in which the flow parameters at the compressor inlet and outlet are measured. Comparison of 3D analysis results with the experimental results shows good agreements. Finally, the current pressure distribution along the pressure side at 50% span is smoothed and considered as the target pressure distribution. The quasi-3D design procedure converges to a new profile after 400 modification steps. The designed impeller is numerically analyzed showing the flow pattern of the impeller is improved and the total to static efficiency of impeller increases by 0.64 percent and the total pressure ratio increased by 3.38 percent.

Pressures beneath the disc of a compensated pressure relief valve for gas/vapour service

1997 ◽  
Vol 211 (4) ◽  
pp. 285-289 ◽  
Author(s):  
P L Betts ◽  
J Francis
Keyword(s):  
Shock Wave ◽  
Pressure Distribution ◽  
Compressible Flow ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Pressure Relief Valve ◽  
Relief Valve ◽  
Pressure Relief ◽  
Valve Disc

In this work, the pressure distribution was measured on the underside of a commercial valve disc ( in situ) when the relief valve was subject to choked compressible flow. The results indicate the limits of three-dimensional effects on the substantially axisymmetric flow. The results also show the position of the minimum section (throat) and shock wave; their behaviour with changing lift is seen to match that inferred from previous work.

Theoretical and Experimental Investigation of Compressible Flow through Convergent–Divergent Nozzles

2012 ◽  
Vol 452-453 ◽  
pp. 1277-1285
Author(s):  
Hocine Mzad ◽  
Mohamed Elguerri
Keyword(s):  
Experimental Investigation ◽  
Mach Number ◽  
Pressure Distribution ◽  
Compressible Flow ◽  
Compressible Flows ◽  
Theoretical Calculations ◽  
Flow Characteristics ◽  
Additional Information ◽  
Shock Location ◽  
Flow Through

The present paper is concerned with the study of compressible flow in a converging-diverging nozzle. From a theoretical and experimental investigation of the flow in an illustrative channel with convergent-divergent area variation, the behavior of the flow along the channel was found to be generally similar in trend to the flow in a stationary convergent-divergent nozzle. In compressible flows, the density and temperature variations are often significant. Therefore, the following study provides additional information on shock location, Mach number behavior and pressure distribution by varying nozzle length. The obtained curves show pressure distribution and Mach number along the two dimensioned nozzles which enable us to compare the experimental data with the theoretical calculations. Furthermore, interesting graphs are plotted which show the relationship between some nozzle parameters and flow characteristics.

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