Airfoil Shape Optimization Using Sensitivity Analysis on Viscous Flow Equations

1993 ◽  
Vol 115 (1) ◽  
pp. 75-84 ◽  
Author(s):  
Mohamed E. Eleshaky ◽  
Oktay Baysal
Keyword(s):  
Shape Optimization ◽  
Stokes Equations ◽  
Prediction Method ◽  
Taylor Series Expansion ◽  
Optimization Method ◽  
Viscous Effects ◽  
Hypersonic Nozzle ◽  
Flow Equations ◽  
Flow Prediction ◽  
Highly Nonlinear

An aerodynamic shape optimization method has previously been developed by the authors using the Euler equations and has been applied to supersonic-hypersonic nozzle designs. This method has also included a flowfield extrapolation (or flow prediction) method based on the Taylor series expansion of an existing CFD solution. The present paper reports on the extension of this method to the thin-layer Navier-Stokes equations in order to account for the viscous effects. Also, to test the method under highly nonlinear conditions, it has been applied to the transonic flows. Initially, the success of the flow prediction method is tested. Then, the overall method is demonstrated by optimizing the shapes of two supercritical transonic airfoils at zero angle of attack. The first one is shape optimized to achieve a minimum drag while obtaining a lift above a specified value. Whereas, the second one is shape optimized for a maximum lift while attaining a drag below a specified value. The results of these two cases indicate that the present method can produce successfully optimized aerodynamic shapes.

Determination of Acoustic Scattering Matrices from Linearized Compressible Flow Equations with Application to Thermoacoustic Stability Analysis

2019 ◽  
Vol 27 (03) ◽  
pp. 1850027 ◽  
Author(s):  
Max Meindl ◽  
Malte Merk ◽  
Fabian Fritz ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Compressible Flow ◽  
Stokes Equations ◽  
Acoustic Scattering ◽  
Scattering Matrix ◽  
Major Influence ◽  
Test Rig ◽  
Viscous Effects ◽  
Flow Equations ◽  
Scattering Matrices

The acoustic transmissions and reflections of plane waves at duct singularities can be represented with so-called scattering matrices. This paper shows how to extract scattering matrices utilizing linearized compressible flow equations and provides a comparative study of different governing equations, namely the Helmholtz, linearized Euler and linearized Navier–Stokes equations. A discontinuous Galerkin finite element method together with a two-source forcing is employed. With this method, the scattering matrix for a radial swirler of a combustion test-rig is computed and validated against the results of a fully compressible Large-Eddy-Simulation. Analogously, the scattering behavior of an axial swirler is investigated. The influence of acoustic-hydrodynamic interactions, viscous effects as well as unsteady boundary layers on the results is investigated for both configurations. A thermoacoustic stability analysis of the combustion test-rig housing the axial swirler is carried out, utilizing the scattering matrix of the swirler. Major influence of the reflections coming from the swirler on the thermoacoustic eigenfrequencies is found.

scholarly journals Blade shape optimization of an aircraft propeller using space mapping surrogates

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986507
Author(s):  
Usama T Toman ◽  
Abdel-Karim SO Hassan ◽  
Farouk M Owis ◽  
Ahmed SA Mohamed
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Shape Optimization ◽  
Stokes Equations ◽  
Optimization Method ◽  
Space Mapping ◽  
High Fidelity ◽  
Blade Shape ◽  
Computational Fluid Dynamics Simulations ◽  
Dynamics Simulations

Propeller performance greatly influences the overall efficiency of the turboprop engines. The aim of this study is to perform a propeller blade shape optimization for maximum aerodynamic efficiency with a minimal number of high-fidelity model evaluations. A physics-based surrogate approach exploiting space mapping is employed for the design process. A space mapping algorithm is utilized, for the first time in the field of propeller design, to link two of the most common propeller analysis models: the classical blade-element momentum theory to be the coarse model; and the high-fidelity computational fluid dynamics tool as the fine model. The numerical computational fluid dynamics simulations are performed using the finite-volume discretization of the Reynolds-averaged Navier–Stokes equations on an adaptive unstructured grid. The optimum design is obtained after few iterations with only 56 computationally expensive computational fluid dynamics simulations. Furthermore, an optimization method based on design of experiments and kriging response surface is used to validate the results and compare the computational efficiency of the two techniques. The results show that space mapping is more computationally efficient.

scholarly journals Revisiting Surface-Subsurface Exchange at Intertidal Zone with a Coupled 2D Hydrodynamic and 3D Variably-Saturated Groundwater Model

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 902
Author(s):  
Zhi Li ◽  
Ben R. Hodges
Keyword(s):  
Intertidal Zone ◽  
Coastal Wetlands ◽  
High Performance ◽  
Stokes Equations ◽  
Wave Model ◽  
Surface Flow ◽  
Richards Equation ◽  
Navier Stokes ◽  
Dynamic Surface ◽  
Flow Equations

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

scholarly journals Tensor Decomposition for Spatial—Temporal Traffic Flow Prediction with Sparse Data

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6046
Author(s):  
Funing Yang ◽  
Guoliang Liu ◽  
Liping Huang ◽  
Cheng Siong Chin
Keyword(s):  
Traffic Flow ◽  
Prediction Method ◽  
Sparse Data ◽  
Time Of Day ◽  
Traffic Prediction ◽  
Traffic Surveillance ◽  
Data Sparsity ◽  
Traffic Flow Prediction ◽  
Flow Prediction ◽  
Sparsity Problem

Urban transport traffic surveillance is of great importance for public traffic control and personal travel path planning. Effective and efficient traffic flow prediction is helpful to optimize these real applications. The main challenge of traffic flow prediction is the data sparsity problem, meaning that traffic flow on some roads or of certain periods cannot be monitored. This paper presents a transport traffic prediction method that leverages the spatial and temporal correlation of transportation traffic to tackle this problem. We first propose to model the traffic flow using a fourth-order tensor, which incorporates the location, the time of day, the day of the week, and the week of the month. Based on the constructed traffic flow tensor, we either propose a model to estimate the correlation in each dimension of the tensor. Furthermore, we utilize the gradient descent strategy to design a traffic flow prediction algorithm that is capable of tackling the data sparsity problem from the spatial and temporal perspectives of the traffic pattern. To validate the proposed traffic prediction method, case studies using real-work datasets are constructed, and the results demonstrate that the prediction accuracy of our proposed method outperforms the baselines. The accuracy decreases the least with the percentage of missing data increasing, including the situation of data being missing on neighboring roads in one or continuous multi-days. This certifies that the proposed prediction method can be utilized for sparse data-based transportation traffic surveillance.

A Three-Dimensional Viscous Transonic Inverse Design Method

2000 ◽  
Author(s):  
W. T. Tiow ◽  
M. Zangeneh
Keyword(s):  
Design Method ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Flow Equations ◽  
Flow Solution ◽  
Turbomachinery Blades ◽  
A Cell ◽  
Inverse Design Method ◽  
Euler Solver

The development and application of a three-dimensional inverse methodology is presented for the design of turbomachinery blades. The method is based on the mass-averaged swirl, rV~θ distribution and computes the necessary blade changes directly from the discrepancies between the target and initial distributions. The flow solution and blade modification converge simultaneously giving the final blade geometry and the corresponding steady state flow solution. The flow analysis is performed using a cell-vertex finite volume time-marching algorithm employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscous effects, dissipative forces are included in the Euler solver using the log-law and mixing length models. The design method can be used with any existing solver solving the same flow equations without any modifications to the blade surface wall boundary condition. Validation of the method has been carried out using a transonic annular turbine nozzle and NASA rotor 67. Finally, the method is demonstrated on the re-design of the blades.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Viscous effects far downstream in a slowly expanding hypersonic nozzle.

AIAA Journal ◽  
1966 ◽  
Vol 4 (5) ◽  
pp. 807-815 ◽  
Author(s):  
MAURICE L. RASMUSSEN ◽  
KRISHNAMURTY KARAMCHETI
Keyword(s):  
Viscous Effects ◽  
Hypersonic Nozzle
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