Results for “PARABOLIC EQUATION” — Page 14

NASA NTRSDate not supplied

Three-Dimensional Nonequilibrium Boundary Layer Stability & Transition Analysis For Martian Entry

In this work, we apply the boundary layer stability code LASTRAC, modified to include chemical and thermal nonequilibrium capabilities, to a simulated test case based on literature, with three-dimensional effects. LASTRAC provides Parabolized Stability Equations (PSE)as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semiempirical eN methods. Tests of the Mars Science Laboratory (MSL)indicated a range of laminar to transitional flow conditions. In order to reduce the weight of Thermal Protection Systems (TPS), reliable prediction of transition and an understanding of the environmental factors that contribute to transition are necessary. This work is a step towards addressing this need, including the effects of thermochemical nonequilibrium but neglecting radiation, ablation, and ionization effects. Our results indicate that an oblique first mode produces maximum N-Factors on the symmetry plane, however with N-Factors too small to explain transition. Although we are able to show nonequilibrium three-dimensional PSE results inCO2, further study with improved mean flow solutions, accounting for some of the uncertainties inherent in this analysis, or evaluation of alternative transition mechanisms is needed to explain transition in the wind tunnel cases examined here.

H L Kline↗

NASA NTRSDate not supplied

Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere using LASTRAC

The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and un-certainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially-laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical eN methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar nondimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.

Heather L Kline↗

NASA NTRS2020

On the Oxidation of the Silicon Bond Coat in Environmental Barrier Coatings

Deal and Grove’s formulation is applied to model the oxidation of the silicon bond coat in environmental barrier coatings. The approach is similar to the author’s previous study, except now the oxidant is assumed to flow through the coating as oxygen ions via vacancies on the oxygen sublattice. The use of an “effective permeability” of the oxidant in the coating is required under the vacancy diffusion assumption. It is found that the linear-parabolic growth equation from Deal and Grove, 2 xox + Axox = Bt , is still applicable for the oxidation of the silicon bond coat, but the equation for the parameter A must be modified to account for the coating. The expression for B is the same as that obtained by Deal and Grove and thus is unaffected by the presence of a coating. The modified expression for A is a linear function of the coating thickness and includes the ratio of the oxidant permeability in the oxide to its effective permeability in the coating

Roy M Sullivan↗

NASA NTRS2021

Pretest Computational Assessment of Boundary Layer Transition in the NASA Juncture Flow Model with an NACA 0015-Based Wing

The first two phases of the NASA Juncture Flow experiment were carried out on a DLR-F6 swept-wing model and were designed to provide “CFD validation-quality” data toward the assessment and improvement of existing CFD turbulence models in predicting onset and extent of three-dimensional separated flow near the wing-juncture trailing-edge region. The next phase of experiments will involve an NACA 0015-based swept wing, as prior risk reduction experiments had indicated that this wing shape resulted in reduced separation near the juncture region than the DLR-F6 wing, thus providing a better option to evaluate the ability of CFD models to predict incipient turbulent separation. The NACA 0015 measurements will also include IR thermography to infer the variation of transition front with respect to an increasing angle of attack. The primary objective of this work is to computationally make a preliminary assessment of the transition front on both surfaces of the NACA 0015 wing at a crank-chord-based Reynolds number of 2.4 x 106 for four different angles of attack, (0°, 2.5°, 5°, and 7.5°) and to determine the dominant mechanisms responsible for transition. This assessment includes both RANS-based transition models from NASA’s OVERFLOW 2.3b flow solver and linear parabolized stability equations (PSE) stability analysis based on the Langley Stability and Transition Analysis code, LASTRAC. Linear PSE results indicate that the upper surface of the wing is dominated by Tollmien- Schlichting (TS) instabilities, and that the laminar flow region shrinks from about 50% chord to a very small region just downstream of the attachment line as the angle of attack is increased from 0° to 7.5°. Consequently, the transition fronts predicted by the Spalart- Allmaras-based amplification factor transport (AFT-2017b) equation model (which accounts for the TS instabilities alone) and the Menter’s shear-stress transport equation (SST2003)- based Langtry-Menter transition model with ability to account for both TS and crossflow effects (LM2015) compare well with those predicted using linear PSE. On the lower surface of the wing, stationary crossflow (CF) instabilities begin to appear on the inboard portion of the wing in addition to the TS-instabilities for the larger angles of attack (5° and 7.5°), further reducing the laminar flow extent within the inboard region. The LM2015 model that accounts for CF effects is able to replicate this trend but appears to predict a slightly earlier transition. The outcome of this effort will inform the experiment and, when the actual experimental data become available, provide further opportunity to assess and improve the various transition models.

CFD modeling↗

NASA NTRS2022

Boundary Layer Instabilities Over a Cone-Cylinder-Flare Model at Mach 6

Computations are performed to investigate the boundary-layer instabilities over a sharp cone-cylinder-flare model at zero degrees angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The geometry consists of a nominally sharp 5-degree half-angle cone, followed by a cylindrical segment and then a 10-degree flare. An axisymmetric separation bubble is generated as a result of the laminar shock/boundary-layer interaction in the cylinder-flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundarylayer edge and the reattachment shock. The predicted heat flux distribution is also in agreement with the measured values downstream of the reattachment location. The analysis of convective and global instabilities is performed for flare half angles equal to 8, 10, and 12 degrees and nosetip radii equal to 0.1, 1, and 5 mm. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations (PSE) and the harmonic linearized Navier-Stokes equations (HLNSE). The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves are compared with the measured spectra at the various locations of the PCB and Kulite sensors. The comparison shows that the computational analysis captures the distinct lobes within the disturbance amplification spectra measured in the experiments, but some differences in amplification characteristics are noted at low frequencies. Overall, the oblique disturbances are found to be more amplified than the planar disturbances. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 degrees. The unstable global mode for the experimental configuration of a 10 degrees flare and a sharp nosetip cone corresponds to a stationary three-dimensional disturbance that is concentrated in the recirculation region and achieves its maximum growth rate for an azimuthal wavenumber of 5.

Hydrodynamic instability↗

NASA NTRS2022

Combined Bluntness and Roughness Effects on Cones at Hypersonic Speeds

This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.

Boundary-layer transition↗

NASA NTRS2022

Stability Analysis of Streaks Induced By Optimized Vortex Generators

Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.

Boundary layer transition↗

NASA NTRSDate not supplied

Transition Modeling Based on the Dual N-factor Method for the CRM-NLF Wind Tunnel Configuration

The dual N-factor method is used to model the boundary-layer transition over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. The paper presents a systematic methodology for transition prediction in the presence of a dual shock system and extends the prior capability for iteratively coupled computational fluid dynamics (CFD) predictions to incorporate three-dimensional, transonic wings. The method employs stability computations based on the linear parabolized stability equations (PSE), along with a dual N-factor criterion. The iterative process begins with the fully turbulent Reynolds-averaged-Navier-Stokes (RANS) mean flow solution. For the first iteration, a mean flow solution is calculated with an imposed transition front that aligns with the shock front from the fully turbulent solution. Subsequently, stability computations are performed along a set of streamlines across the wing to calculate the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) modes. The transition criterion based on the dual N-factor method is used to infer the updated transition front and the process is successively repeated until convergence of the solution. Within three iterations, the predicted fronts for angles of attack of 1.45, 1.98, 2.46 and 2.94 degrees and a mean-aerodynamic-chord Reynolds number equal to 15 million, approach visual convergence in most regions of the studied cases, and the resulting predictions are in good agreement with the transition fronts deduced from measurements of temperature-sensitive paint. Even though surface pressure measurements based on fully-turbulent flow agree well with the measured pressure coefficient distributions, strong viscous-inviscid interaction effects cause significant shifts in the shock locations based on the imposed transition front, underscoring the intrusive nature of static pressure measurements using surface mounted ports on the CRM-NLF configuration.

Boundary Layer Transition↗

NASA NTRSDate not supplied

Effects of Random Micron-Sized Roughness on Swept-Wing Transition

This study examines the effect of random micron-sized distributed roughness on stationary crossflow instabilities. The roughness parameters are varied by creating nanoparticle coatings of various formulations and applying them to inserts that cover approximately the first 14% of the model. In addition to the baseline configuration (no added roughness, root-mean-square (RMS) ≈ 0.42 𝜇m), panels with RMS roughness values of 4.8 and 8.6 𝜇m were tested, with correlation lengths of 1029 and 385 𝜇m, respectively. Despite the significant roughness levels tested, the transition location was found to be only mildly impacted by the additional roughness, and the roughness panel with lower RMS amplitude caused a larger upstream movement of transition, on average. However, the stationary crossflow amplitudes and wavelength content were found to vary substantially depending on the roughness input. In particular, the panel with higher RMS roughness amplitude resulted in significantly larger amplitudes in the 7.5-9 mm wavelength range at the farthest upstream measurement station, while the lower roughness panel resulted in mildly larger amplitudes at 10 mm and wavelengths larger than 15 mm. Nonlinear Parabolized Stability Equations (PSE) computations were performed to attempt to estimate the initial amplitudes of the stationary crossflow instabilities. Wavelength spectra were matched at the most upstream measurement location, but large discrepancies exist between the predicted and measured growth behavior farther downstream, thus, more work is required to improve confidence in initial amplitude estimates.

boundary-layer transition↗

NASA NTRSDate not supplied

Effects of Random Micron-Sized Roughness on Swept-Wing Transition

This study examines the effect of random micron-sized distributed roughness on stationary crossflow instabilities. The roughness parameters are varied by creating nanoparticle coatings of various formulations and applying them to inserts that cover approximately the first 14% of the model. In addition to the baseline configuration (no added roughness, root-mean-square (RMS) ≈ 0.42 𝜇m), panels with RMS roughness values of 4.8 and 8.6 𝜇m were tested, with correlation lengths of 1029 and 385 𝜇m, respectively. Despite the significant roughness levels tested, the transition location was found to be only mildly impacted by the additional roughness, and the roughness panel with lower RMS amplitude caused a larger upstream movement of transition, on average. However, the stationary crossflow amplitudes and wavelength content were found to vary substantially depending on the roughness input. In particular, the panel with higher RMS roughness amplitude resulted in significantly larger amplitudes in the 7.5-9 mm wavelength range at the farthest upstream measurement station, while the lower roughness panel resulted in mildly larger amplitudes at 10 mm and wavelengths larger than 15 mm. Nonlinear Parabolized Stability Equations (PSE) computations were performed to attempt to estimate the initial amplitudes of the stationary crossflow instabilities. Wavelength spectra were matched at the most upstream measurement location, but large discrepancies exist between the predicted and measured growth behavior farther downstream, thus, more work is required to improve confidence in initial amplitude estimates.

boundary-layer transition↗

NASA NTRSDate not supplied

Effects of Random Micron-Sized Roughness on Swept-Wing Transition

This study examines the effect of random micron-sized distributed roughness on stationary crossflow instabilities. The roughness parameters are varied by creating nanoparticle coatings of various formulations and applying them to inserts that cover approximately the first 14% of the model. In addition to the baseline configuration (no added roughness, root-mean-square (RMS) ≈ 0.42 𝜇m), panels with RMS roughness values of 4.8 and 8.6 𝜇m were tested, with correlation lengths of 1029 and 385 𝜇m, respectively. Despite the significant roughness levels tested, the transition location was found to be only mildly impacted by the additional roughness, and the roughness panel with lower RMS amplitude caused a larger upstream movement of transition, on average. However, the stationary crossflow amplitudes and wavelength content were found to vary substantially depending on the roughness input. In particular, the panel with higher RMS roughness amplitude resulted in significantly larger amplitudes in the 7.5-9 mm wavelength range at the farthest upstream measurement station, while the lower roughness panel resulted in mildly larger amplitudes at 10 mm and wavelengths larger than 15 mm. Nonlinear Parabolized Stability Equations (PSE) computations were performed to attempt to estimate the initial amplitudes of the stationary crossflow instabilities. Wavelength spectra were matched at the most upstream measurement location, but large discrepancies exist between the predicted and measured growth behavior farther downstream, thus, more work is required to improve confidence in initial amplitude estimates.

boundary-layer transition↗

NASA NTRSDate not supplied

Computational Study of Low-Speed Boundary-Layer Laminar-Turbulent Transition over a 30º Swept Plate in a Channel

Reliable boundary-layer laminar-turbulent transition predictions are critical for the design of aircraft that use natural or controlled laminar flow to achieve low drag and better fuel efficiency. During cruise flight through low turbulence, the three-dimensional boundary layer over swept surfaces can transition prematurely due to stationary crossflow instabilities induced by surface roughness. Parabolized stability equations analyses have been successfully used to explain the different phases of the transition process under well controlled perturbations such as steps or discrete roughness elements. However, methodologies are still lacking to model the boundary layer receptivity to distributed random roughness, and the following non-linear instability stages leading to transition. For engineering applications, several semi-empirical methods based on linear amplification factors or local helicity have found growing adoption, but their reliability is limited by their level of simplification and the sparsity of data they are based on. To address this gap, a new study of the effect of distributed random surface roughness on crossflow transition was started, using a 30◦ swept plate as a test vehicle. The plate, which is mounted in the 2 Foot × 3 Foot Low-Speed Boundary-Layer Channel at the NASA Langley Research Center, has been tested with micro-scale roughness of varied geometry near the leading edge. In order to analyze the flow in the test section and prepare Direct Numerical Simulations with resolved roughness, Reynolds-Averaged Navier-Stokes (RANS) simulations of the flow over the plate installed in the wind tunnel test section were performed using the Langtry-Menter transition model with stationary crossflow extension. This paper presents the results of these simulations, with comparison to the experiment.

ARMD↗

NASA NTRSDate not supplied

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

boundary-layer transition↗

NASA NTRSDate not supplied

Ground Tests on the BOLT Geometry at Mach 7: Cross-Facility Comparison and Stability Analysis

Transition measurements have been obtained through two experimental campaigns conducted independently by the German Aerospace Center and the French Aerospace Lab with the French Alternative Energies and Atomic Energy Commission on subscale models of the BOLT-1 flight experiment geometry. This paper details a cross-facility comparison of measurements obtained at Mach 7, as well as subsequent computational analysis. Infrared (IR) thermography measurements obtained by both campaigns have facilitated a global comparison of the transition front across facilities at analagous conditions, which are found to be in good agreement. High-frequency surface pressure fluctuation data demonstrate significant amplification of instabilities with Mack-mode characteristics in the outboard regions of the acreage. These measurements are compared to stability analyses of varying fidelity. The computational methods employed to characterize the boundary-layer transition phenomena include the traditional line-marching implementation of the Parabolized Stability Equations (PSE), 2D eigenvalue analysis coupled with PSE, and Adaptive Mesh Refinement Wavepacket Tracking. While the 2D eigenvalue analysis is found to predict instabilities, which correlate in terms of frequency and acreage location to the experimental measurements, the predicted amplification for these instabilities is lower than would typically be expected for transition. Line-marching results for traveling crossflow produce the best match to the experimental transition front, with a consistent transition N factor of approximately 3-3.5.

Boundary Layer Transition↗

NASA NTRSDate not supplied

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

computational modeling↗

NASA NTRS1981

A Quasi-Parabolic technique for computation of three-dimensional viscous flows

A computational technique is presented for obtaining flowfield solutions to a parabolic form of the Navier-Stokes equations. The point of departure is the General Interpolant Method (GIM) which provides a discretization for partial differential equations on arbitrary three-dimensional geometries. The new scheme, termed Quasi-Parabolic, treats the parabolized equations but with 'time-like' terms appended. Addition of these extra terms, which are relaxed by iteration, avoid many of the singularities inherent in classical parabolic Navier-Stokes methods. Streamwise derivatives are approximated by three-point backward differences and the cross plane operators use an alternating forward-backward sweep. A two-step sequence is used to implement the difference scheme in the spatial dimensions and a time-like relaxation converges the quasi-parabolic procedure at each plane. Solutions are presented for flows in two and three dimensions. Inviscid flows are solved for internal and external applications and viscous flows in boundary layers and free shear layers are also computed with the GIM/Quasi-Parabolic scheme.

Spradley, L. W.↗

NASA NTRS1976

A finite element solution of unsteady transonic flow problems for three-dimensional wings and bodies

A computerized finite element method has been developed to solve a form of the three-dimensional inviscid, irrotational unsteady transonic equation for pointed and rectangular wings and wing-body combinations. The equation is a 'parabolized' version of the full unsteady transonic equation which includes the effect of the advancing wave and the acceleration in the steady flow field thus including a thickness effect. Automatic mesh generation using conformal mapping has the advantage of allowing relatively arbitrary cross-sections to be closely approximated while taking advantage of the body's similarity to a more simple configuration. Plunge, pitch, and roll modes are computed

Kimble, K. R.↗

NASA NTRS1996

Development of Multiobjective Optimization Techniques for Sonic Boom Minimization

A discrete, semi-analytical sensitivity analysis procedure has been developed for calculating aerodynamic design sensitivities. The sensitivities of the flow variables and the grid coordinates are numerically calculated using direct differentiation of the respective discretized governing equations. The sensitivity analysis techniques are adapted within a parabolized Navier Stokes equations solver. Aerodynamic design sensitivities for high speed wing-body configurations are calculated using the semi-analytical sensitivity analysis procedures. Representative results obtained compare well with those obtained using the finite difference approach and establish the computational efficiency and accuracy of the semi-analytical procedures. Multidisciplinary design optimization procedures have been developed for aerospace applications namely, gas turbine blades and high speed wing-body configurations. In complex applications, the coupled optimization problems are decomposed into sublevels using multilevel decomposition techniques. In cases with multiple objective functions, formal multiobjective formulation such as the Kreisselmeier-Steinhauser function approach and the modified global criteria approach have been used. Nonlinear programming techniques for continuous design variables and a hybrid optimization technique, based on a simulated annealing algorithm, for discrete design variables have been used for solving the optimization problems. The optimization procedure for gas turbine blades improves the aerodynamic and heat transfer characteristics of the blades. The two-dimensional, blade-to-blade aerodynamic analysis is performed using a panel code. The blade heat transfer analysis is performed using an in-house developed finite element procedure. The optimization procedure yields blade shapes with significantly improved velocity and temperature distributions. The multidisciplinary design optimization procedures for high speed wing-body configurations simultaneously improve the aerodynamic, the sonic boom and the structural characteristics of the aircraft. The flow solution is obtained using a comprehensive parabolized Navier Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. The aircraft wing load carrying member is modeled as either an isotropic or a composite box beam. The isotropic box beam is analyzed using thin wall theory. The composite box beam is analyzed using a finite element procedure. The developed optimization procedures yield significant improvements in all the performance criteria and provide interesting design trade-offs. The semi-analytical sensitivity analysis techniques offer significant computational savings and allow the use of comprehensive analysis procedures within design optimization studies.

Chattopadhyay, Aditi↗