Validation and verification benchmark test cases are employed in computational fluid dynamics (CFD) to determine the best practices in application of various CFD tools. These cases focus on the geometry modeling, mesh generation, numerical algorithms, and turbulence models to ensure consistent and accurate numerical simulation of physical phenomena. Assessing model accuracy is essential to identify areas of improvement in various turbulence models. Flow past several symmetric NACA airfoils, namely NACA 0012, NACA 0015 and NACA 0018 are standard test cases for validating and evaluating turbulence models’ accuracy since the experimental data is available for these airfoils. Available wind tunnel data allows for testing turbulence models’ capability to predict lift, drag, and pressure distributions for various angles of attack ranging at high Reynolds numbers. In this study, two turbulence models are compared to experimental data for the NACA 0012, 0015, and 0018 airfoils. The two turbulence models are the well-known one equation Spalart-Allmaras (SA) and the recently developed Wray-Agarwal (WA) model. Numerical results show that both turbulence models are capable of accurately predicting lift and pressure coefficients but generally over predict drag. However, the WA model exhibits higher accuracy in predicting lift at high angles of attack for two of the airfoils and peak pressure for NACA 0012 airfoil.
The Wray-Agarwal Algebraic Transition (WA-AT) model is a recently proposed new transition model with the goal to obtain similar level or better accuracy with substantially less computational cost compared to existing three (k-kl-ω) or four ( ) equation transition models. The WA-AT model uses the wall distance free version of WA turbulence model (WA2018) in combination with an algebraic transition model. The model has been previously validated for various ERCOFTAC benchmark flat plate cases and for some aerodynamic bodies. To further validate this model, the transitional flows past NACA 0012, 0015, and 0018 airfoils are simulated for a range of Reynolds numbers, turbulence intensities, and angles of attack in ANSYS Fluent. The NACA airfoil cases are simulated at angles of attack from zero to ten degrees, and Reynolds numbers ranging from to , and turbulence intensities ranging from 0.07% to 0.3%. The validation studies show similar or improved predictions using the WA-AT model over the Langtry-Menter’s four equation transition-SST (k –ω – γ - Reθt) model for pressure, drag, lift, and transition location. Overall, the results demonstrate that the WA-AT model offers similar or better accuracy as the four-equation transition-SST model for simulation of transitional flow over NACA 0012, 0015, and 0018 airfoils at much less computational cost.
In NASA’s High Fidelity CFD Workshop 2022, the Joukowski airfoil was identified as a benchmark verification case to test the convergence behavior of different turbulence models in different CFD solvers with particular emphasis on SA-neg-QCR 2000 turbulence model. This thesis also studies the accuracy and convergence behavior of Wray-Agarwal (WA) and Spalart-Allmaras (SA) one equation turbulence models by computing the flow past Joukowski airfoil on a sequence of seven workshop specified grids from coarse to fine. The benchmark case has free stream Mach number of 0.15, chord Reynolds number of 3x106 and angle of attack of 0 degree. The goal is to evaluate the convergence behavior of drag coefficient on a sequence of seven grids using WA and original version of SA model in ANSYS Fluent. Both models exhibit nearly first order convergence rates for first order solutions and second order convergence rates for second order solutions. There is no notable difference in the convergence rates between the two turbulence models for both first order and second order implementations.
","abstract_html":"<p> Validation and verification benchmark test cases are employed in computational fluid dynamics (CFD) to determine the best practices in application of various CFD tools. These cases focus on the geometry modeling, mesh generation, numerical algorithms, and turbulence models to ensure consistent and accurate numerical simulation of physical phenomena. Assessing model accuracy is essential to identify areas of improvement in various turbulence models. Flow past several symmetric NACA airfoils, namely NACA 0012, NACA 0015 and NACA 0018 are standard test cases for validating and evaluating turbulence models’ accuracy since the experimental data is available for these airfoils. Available wind tunnel data allows for testing turbulence models’ capability to predict lift, drag, and pressure distributions for various angles of attack ranging at high Reynolds numbers. In this study, two turbulence models are compared to experimental data for the NACA 0012, 0015, and 0018 airfoils. The two turbulence models are the well-known one equation Spalart-Allmaras (SA) and the recently developed Wray-Agarwal (WA) model. Numerical results show that both turbulence models are capable of accurately predicting lift and pressure coefficients but generally over predict drag. However, the WA model exhibits higher accuracy in predicting lift at high angles of attack for two of the airfoils and peak pressure for NACA 0012 airfoil.</p> <p> The Wray-Agarwal Algebraic Transition (WA-AT) model is a recently proposed new transition model with the goal to obtain similar level or better accuracy with substantially less computational cost compared to existing three (<em>k-kl-ω) </em>or four ( ) equation transition models. The WA-AT model uses the wall distance free version of WA turbulence model (WA2018) in combination with an algebraic transition model. The model has been previously validated for various ERCOFTAC benchmark flat plate cases and for some aerodynamic bodies. To further validate this model, the transitional flows past NACA 0012, 0015, and 0018 airfoils are simulated for a range of Reynolds numbers, turbulence intensities, and angles of attack in ANSYS Fluent. The NACA airfoil cases are simulated at angles of attack from zero to ten degrees, and Reynolds numbers ranging from to , and turbulence intensities ranging from 0.07% to 0.3%. The validation studies show similar or improved predictions using the WA-AT model over the Langtry-Menter’s four equation transition-SST (<em>k –ω – γ - Re<sub>θt</sub></em>) model for pressure, drag, lift, and transition location. Overall, the results demonstrate that the WA-AT model offers similar or better accuracy as the four-equation transition-SST model for simulation of transitional flow over NACA 0012, 0015, and 0018 airfoils at much less computational cost. </p> <p> In NASA’s High Fidelity CFD Workshop 2022, the Joukowski airfoil was identified as a benchmark verification case to test the convergence behavior of different turbulence models in different CFD solvers with particular emphasis on SA-neg-QCR 2000 turbulence model. This thesis also studies the accuracy and convergence behavior of Wray-Agarwal (WA) and Spalart-Allmaras (SA) one equation turbulence models by computing the flow past Joukowski airfoil on a sequence of seven workshop specified grids from coarse to fine. The benchmark case has free stream Mach number of 0.15, chord Reynolds number of 3x10<sup>6</sup> and angle of attack of 0 degree. The goal is to evaluate the convergence behavior of drag coefficient on a sequence of seven grids using WA and original version of SA model in ANSYS Fluent. Both models exhibit nearly first order convergence rates for first order solutions and second order convergence rates for second order solutions. There is no notable difference in the convergence rates between the two turbulence models for both first order and second order implementations.</p>","abstract_has_math":false,"creators":["Ryan-Simmons, Dean"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Mechanical Engineering & Materials Science","degree_department":null,"school":null,"contributors":["Ramesh Agarwal","Swami Karunamoorthy David Peters"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-10-01T07:00:00Z","date_published":"2022-10-01T07:00:00Z","updated_at":"2026-07-24T06:13:14Z","subjects":["CFD Airfoil Validation Verification External Flow Computational Fluid Dynamics","Aerodynamics and Fluid Mechanics","Engineering"],"languages":["English (en)"],"rights":["I have not registered my thesis with the U.S. Copyright Office, but intend to later."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/eng_etds/770"],"render_values":[{"text":"https://openscholarship.wustl.edu/eng_etds/770","href":"https://openscholarship.wustl.edu/eng_etds/770","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/g08w-3458","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ramesh Agarwal","Swami Karunamoorthy David Peters"]},{"key":"dc:creator","label":"Author","values":["Ryan-Simmons, Dean"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-12-16T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering & Materials Science","McKelvey School of Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["CFD Airfoil Validation Verification External Flow Computational Fluid Dynamics","Aerodynamics and Fluid Mechanics","Engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]},{"key":"dc:rights","label":"Dc Rights","values":["I have not registered my thesis with the U.S. Copyright Office, but intend to later."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/g08w-3458","https://openscholarship.wustl.edu/eng_etds/770"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Validation and verification benchmark test cases are employed in computational fluid dynamics (CFD) to determine the best practices in application of various CFD tools. These cases focus on the geometry modeling, mesh generation, numerical algorithms, and turbulence models to ensure consistent and accurate numerical simulation of physical phenomena. Assessing model accuracy is essential to identify areas of improvement in various turbulence models. Flow past several symmetric NACA airfoils, namely NACA 0012, NACA 0015 and NACA 0018 are standard test cases for validating and evaluating turbulence models’ accuracy since the experimental data is available for these airfoils. Available wind tunnel data allows for testing turbulence models’ capability to predict lift, drag, and pressure distributions for various angles of attack ranging at high Reynolds numbers. In this study, two turbulence models are compared to experimental data for the NACA 0012, 0015, and 0018 airfoils. The two turbulence models are the well-known one equation Spalart-Allmaras (SA) and the recently developed Wray-Agarwal (WA) model. Numerical results show that both turbulence models are capable of accurately predicting lift and pressure coefficients but generally over predict drag. However, the WA model exhibits higher accuracy in predicting lift at high angles of attack for two of the airfoils and peak pressure for NACA 0012 airfoil.
The Wray-Agarwal Algebraic Transition (WA-AT) model is a recently proposed new transition model with the goal to obtain similar level or better accuracy with substantially less computational cost compared to existing three (k-kl-ω) or four ( ) equation transition models. The WA-AT model uses the wall distance free version of WA turbulence model (WA2018) in combination with an algebraic transition model. The model has been previously validated for various ERCOFTAC benchmark flat plate cases and for some aerodynamic bodies. To further validate this model, the transitional flows past NACA 0012, 0015, and 0018 airfoils are simulated for a range of Reynolds numbers, turbulence intensities, and angles of attack in ANSYS Fluent. The NACA airfoil cases are simulated at angles of attack from zero to ten degrees, and Reynolds numbers ranging from to , and turbulence intensities ranging from 0.07% to 0.3%. The validation studies show similar or improved predictions using the WA-AT model over the Langtry-Menter’s four equation transition-SST (k –ω – γ - Reθt) model for pressure, drag, lift, and transition location. Overall, the results demonstrate that the WA-AT model offers similar or better accuracy as the four-equation transition-SST model for simulation of transitional flow over NACA 0012, 0015, and 0018 airfoils at much less computational cost.
In NASA’s High Fidelity CFD Workshop 2022, the Joukowski airfoil was identified as a benchmark verification case to test the convergence behavior of different turbulence models in different CFD solvers with particular emphasis on SA-neg-QCR 2000 turbulence model. This thesis also studies the accuracy and convergence behavior of Wray-Agarwal (WA) and Spalart-Allmaras (SA) one equation turbulence models by computing the flow past Joukowski airfoil on a sequence of seven workshop specified grids from coarse to fine. The benchmark case has free stream Mach number of 0.15, chord Reynolds number of 3x106 and angle of attack of 0 degree. The goal is to evaluate the convergence behavior of drag coefficient on a sequence of seven grids using WA and original version of SA model in ANSYS Fluent. Both models exhibit nearly first order convergence rates for first order solutions and second order convergence rates for second order solutions. There is no notable difference in the convergence rates between the two turbulence models for both first order and second order implementations.
"]},{"key":"dc:title","label":"Title","values":["Validation and Verification of the Wray-Agarwal Turbulence and Algebraic Transition Models for 2D External Airfoil Flows"]}]}],"canonical_facts":{"dc:contributor":["Ramesh Agarwal","Swami Karunamoorthy David Peters"],"dc:creator":["Ryan-Simmons, Dean"],"dc:date.available":["2022-12-16T08:00:00Z"],"dc:description.abstract":["Validation and verification benchmark test cases are employed in computational fluid dynamics (CFD) to determine the best practices in application of various CFD tools. These cases focus on the geometry modeling, mesh generation, numerical algorithms, and turbulence models to ensure consistent and accurate numerical simulation of physical phenomena. Assessing model accuracy is essential to identify areas of improvement in various turbulence models. Flow past several symmetric NACA airfoils, namely NACA 0012, NACA 0015 and NACA 0018 are standard test cases for validating and evaluating turbulence models’ accuracy since the experimental data is available for these airfoils. Available wind tunnel data allows for testing turbulence models’ capability to predict lift, drag, and pressure distributions for various angles of attack ranging at high Reynolds numbers. In this study, two turbulence models are compared to experimental data for the NACA 0012, 0015, and 0018 airfoils. The two turbulence models are the well-known one equation Spalart-Allmaras (SA) and the recently developed Wray-Agarwal (WA) model. Numerical results show that both turbulence models are capable of accurately predicting lift and pressure coefficients but generally over predict drag. However, the WA model exhibits higher accuracy in predicting lift at high angles of attack for two of the airfoils and peak pressure for NACA 0012 airfoil.
The Wray-Agarwal Algebraic Transition (WA-AT) model is a recently proposed new transition model with the goal to obtain similar level or better accuracy with substantially less computational cost compared to existing three (k-kl-ω) or four ( ) equation transition models. The WA-AT model uses the wall distance free version of WA turbulence model (WA2018) in combination with an algebraic transition model. The model has been previously validated for various ERCOFTAC benchmark flat plate cases and for some aerodynamic bodies. To further validate this model, the transitional flows past NACA 0012, 0015, and 0018 airfoils are simulated for a range of Reynolds numbers, turbulence intensities, and angles of attack in ANSYS Fluent. The NACA airfoil cases are simulated at angles of attack from zero to ten degrees, and Reynolds numbers ranging from to , and turbulence intensities ranging from 0.07% to 0.3%. The validation studies show similar or improved predictions using the WA-AT model over the Langtry-Menter’s four equation transition-SST (k –ω – γ - Reθt) model for pressure, drag, lift, and transition location. Overall, the results demonstrate that the WA-AT model offers similar or better accuracy as the four-equation transition-SST model for simulation of transitional flow over NACA 0012, 0015, and 0018 airfoils at much less computational cost.
In NASA’s High Fidelity CFD Workshop 2022, the Joukowski airfoil was identified as a benchmark verification case to test the convergence behavior of different turbulence models in different CFD solvers with particular emphasis on SA-neg-QCR 2000 turbulence model. This thesis also studies the accuracy and convergence behavior of Wray-Agarwal (WA) and Spalart-Allmaras (SA) one equation turbulence models by computing the flow past Joukowski airfoil on a sequence of seven workshop specified grids from coarse to fine. The benchmark case has free stream Mach number of 0.15, chord Reynolds number of 3x106 and angle of attack of 0 degree. The goal is to evaluate the convergence behavior of drag coefficient on a sequence of seven grids using WA and original version of SA model in ANSYS Fluent. Both models exhibit nearly first order convergence rates for first order solutions and second order convergence rates for second order solutions. There is no notable difference in the convergence rates between the two turbulence models for both first order and second order implementations.
"],"dc:identifier":["https://doi.org/10.7936/g08w-3458","https://openscholarship.wustl.edu/eng_etds/770"],"dc:language":["English (en)"],"dc:rights":["I have not registered my thesis with the U.S. Copyright Office, but intend to later."],"dc:subject":["CFD Airfoil Validation Verification External Flow Computational Fluid Dynamics","Aerodynamics and Fluid Mechanics","Engineering"],"dc:title":["Validation and Verification of the Wray-Agarwal Turbulence and Algebraic Transition Models for 2D External Airfoil Flows"],"thesis:degree_discipline":["Mechanical Engineering & Materials Science","McKelvey School of Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T06:13:14Z"}