L.L.M. Veldhuis
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44 records found
1
An Experimental Investigation of an Infinite Wing in Ground Effect
Quantifying the Influence of Ground Proximity on Steady and Unsteady Lift Response
The investigation initially establishes a steady-state baseline, revealing that ground influence is non-monotonic. At large clearances (H>0.8), the flow is largely unaffected by the presence of the ground. At moderate clearances (0.4<H≤0.8), lift enhancement is driven by the Venturi effect, where geometric confinement accelerates the underbody flow. In extreme ground effect ($H≤0.4$), a viscous-confinement domain is observed. In this state, the interaction between the airfoil and ground-plane boundary layers induces a pressure-side blockage that caps circulation growth, a phenomenon that contradicts classical inviscid predictions.
In the unsteady domain, the airfoil was subjected to sinusoidal pitching across a matrix of reduced frequencies (k=0.05 to 0.20) and ground clearances (H=0.1 to ∞). In attached-flow conditions, ground proximity modulates the convective time lag of the wake. At intermediate heights, the accelerated gap flow reduces the time required for circulation to equilibrate, effectively compressing the lift hysteresis loops. At H=0.2, physical blockage and air-column stiffening significantly widen the hysteresis loops, indicating a substantial increase in phase lag relative to freestream conditions.
The most significant findings emerge in the dynamic stall domain. The presence of the ground plane serves as a powerful stabilising mechanism. By imposing a vertical geometric constraint, the wall suppresses the coherent roll-up and subsequent shedding of the Leading-Edge Vortex (LEV). This suppression of discrete vortex shedding replaces abrupt load collapses characteristic of classical dynamic stall with geometrically constrained separation. This transition results in a marked increase in aerodynamic damping, suggesting that ground proximity inherently mitigates the energy extraction mechanisms that typically trigger instabilities.
This work demonstrates that the non-dimensional height must be considered as a primary kinematic parameter, and reduced frequency alone is insufficient to characterise unsteady stall in ground effect. These insights provide a quantitative foundation for the development of active aerodynamic control systems and offer a physical explanation for the suppression of porpoising in high-downforce racing applications and low-flying vehicles. ...
The investigation initially establishes a steady-state baseline, revealing that ground influence is non-monotonic. At large clearances (H>0.8), the flow is largely unaffected by the presence of the ground. At moderate clearances (0.4<H≤0.8), lift enhancement is driven by the Venturi effect, where geometric confinement accelerates the underbody flow. In extreme ground effect ($H≤0.4$), a viscous-confinement domain is observed. In this state, the interaction between the airfoil and ground-plane boundary layers induces a pressure-side blockage that caps circulation growth, a phenomenon that contradicts classical inviscid predictions.
In the unsteady domain, the airfoil was subjected to sinusoidal pitching across a matrix of reduced frequencies (k=0.05 to 0.20) and ground clearances (H=0.1 to ∞). In attached-flow conditions, ground proximity modulates the convective time lag of the wake. At intermediate heights, the accelerated gap flow reduces the time required for circulation to equilibrate, effectively compressing the lift hysteresis loops. At H=0.2, physical blockage and air-column stiffening significantly widen the hysteresis loops, indicating a substantial increase in phase lag relative to freestream conditions.
The most significant findings emerge in the dynamic stall domain. The presence of the ground plane serves as a powerful stabilising mechanism. By imposing a vertical geometric constraint, the wall suppresses the coherent roll-up and subsequent shedding of the Leading-Edge Vortex (LEV). This suppression of discrete vortex shedding replaces abrupt load collapses characteristic of classical dynamic stall with geometrically constrained separation. This transition results in a marked increase in aerodynamic damping, suggesting that ground proximity inherently mitigates the energy extraction mechanisms that typically trigger instabilities.
This work demonstrates that the non-dimensional height must be considered as a primary kinematic parameter, and reduced frequency alone is insufficient to characterise unsteady stall in ground effect. These insights provide a quantitative foundation for the development of active aerodynamic control systems and offer a physical explanation for the suppression of porpoising in high-downforce racing applications and low-flying vehicles.
On-site Experimental Investigation of Full-Scale Truck Wheel Wake
Application of ‘Ring of Fire’ for Flow Field Characterization and Wake-Rake Validation
This study addresses this limitation by applying the non-intrusive “Ring of Fire” measurement technique to reconstruct the three-dimensional front wheel wake of a full-scale truck. The objective was to design and implement a Ring of Fire setup capable of resolving the wheel wake region to support CFD validation, while also evaluating the conventional wake-rake method.
The Ring of Fire measurement technique is based on Particle Image Velocimetry (PIV). Helium-Filled Soap Bubbles (HFSBs) served as tracer particles, illuminated by high-power LEDs and recorded by high-speed cameras. A Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm reconstructed three-dimensional particle trajectories, from which velocity fields were derived. For comparison, a wake-rake equipped with Kiel probes measured a two-dimensional total pressure field in the wheel wake.
Experiments were conducted on a test track using a full-scale European cab-over-engine tractor–trailer combination. Two configurations were tested: a baseline (Variant A) and a reduced-aero configuration (Variant B). Containing the HFSBs in an outdoor environment was a major challenge and was addressed using a foldable dome tent housing three vertically oriented LED units and a seeding rake. Four high speed cameras recorded the motion of the HFSBs within a measurement domain extending 1 meter from the truck surface and up to 1 meter in height, covering the longitudinal distance of 2.2 meter. A dedicated run procedure ensured synchronization between dome opening and data acquisition during truck passage.
A total of 100 runs were performed over two days. 8 valid runs for Variant A and 21 for Variant B were processed after excluding invalid measurements. Crosswind effects were assessed using conditional averaging and were found to be negligible within measurement uncertainty. Convergence analysis indicated that at least 16 combined runs were required to achieve a stable, time-averaged flow field with over 95% spatial data coverage.
For both configurations, the wheel wake region, characterized by significant reduced velocity magnitude, emerged downstream of the footstep and expanded further downstream. Overall, Variant A showed a larger wake region.
Comparison with wake-rake results revealed similar wake topology, but the Ring of Fire provided higher spatial resolution and full three-dimensional reconstruction. The study demonstrates that the Ring of Fire technique successfully captures the complete front wheel wake of a full-scale truck and offers substantial advantages over conventional planar wake-rake measurements. ...
This study addresses this limitation by applying the non-intrusive “Ring of Fire” measurement technique to reconstruct the three-dimensional front wheel wake of a full-scale truck. The objective was to design and implement a Ring of Fire setup capable of resolving the wheel wake region to support CFD validation, while also evaluating the conventional wake-rake method.
The Ring of Fire measurement technique is based on Particle Image Velocimetry (PIV). Helium-Filled Soap Bubbles (HFSBs) served as tracer particles, illuminated by high-power LEDs and recorded by high-speed cameras. A Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm reconstructed three-dimensional particle trajectories, from which velocity fields were derived. For comparison, a wake-rake equipped with Kiel probes measured a two-dimensional total pressure field in the wheel wake.
Experiments were conducted on a test track using a full-scale European cab-over-engine tractor–trailer combination. Two configurations were tested: a baseline (Variant A) and a reduced-aero configuration (Variant B). Containing the HFSBs in an outdoor environment was a major challenge and was addressed using a foldable dome tent housing three vertically oriented LED units and a seeding rake. Four high speed cameras recorded the motion of the HFSBs within a measurement domain extending 1 meter from the truck surface and up to 1 meter in height, covering the longitudinal distance of 2.2 meter. A dedicated run procedure ensured synchronization between dome opening and data acquisition during truck passage.
A total of 100 runs were performed over two days. 8 valid runs for Variant A and 21 for Variant B were processed after excluding invalid measurements. Crosswind effects were assessed using conditional averaging and were found to be negligible within measurement uncertainty. Convergence analysis indicated that at least 16 combined runs were required to achieve a stable, time-averaged flow field with over 95% spatial data coverage.
For both configurations, the wheel wake region, characterized by significant reduced velocity magnitude, emerged downstream of the footstep and expanded further downstream. Overall, Variant A showed a larger wake region.
Comparison with wake-rake results revealed similar wake topology, but the Ring of Fire provided higher spatial resolution and full three-dimensional reconstruction. The study demonstrates that the Ring of Fire technique successfully captures the complete front wheel wake of a full-scale truck and offers substantial advantages over conventional planar wake-rake measurements.
Assessment of a GPU accelerated Cartesian Fast Multipole Method
Accuracy and performance analysis of Cartesian FMM applied on the vortex particle method
Inline with the increasing adoption of GPUs in performing scientific computations, the solver developed assigns computationally heavy tasks to parallelised execution on the CPU or GPU, using the taichi compiler. The accompanying introduction of reduced floating point accuracy introduces new considerations for the accuracy of the method when performed on the GPU. Error quantification is performed on a single timestep for a range of flow scenarios, with an emphasis on the effect of main FMM parameters on accuracy. Results indicate a positive impact of increasing the Taylor series truncation order on FMM accuracy, up to a plateau caused by the accumulation of rounding errors. The octree depth was found to have low impact on the accuracy. Validation of the solver is performed through underresolved direct numerical simulation (DNS) of Lamb-Oseen vortex, vortex ring, and colliding vortex ring test cases. The impact of FMM on particle velocities and positions throughout simulations is measured, and key flow diagnostics are provided, indicating minimal FMM impact on the physical validity of simulations.
More chaotic flows exhibited an unbounded nature of FMM error growth while low Reynolds number flows counteracted the FMM error. The performance of the main operations of the solver was profiled, highlighting trade-offs between speed and accuracy, and indicating areas for future performance improvements. ...
Inline with the increasing adoption of GPUs in performing scientific computations, the solver developed assigns computationally heavy tasks to parallelised execution on the CPU or GPU, using the taichi compiler. The accompanying introduction of reduced floating point accuracy introduces new considerations for the accuracy of the method when performed on the GPU. Error quantification is performed on a single timestep for a range of flow scenarios, with an emphasis on the effect of main FMM parameters on accuracy. Results indicate a positive impact of increasing the Taylor series truncation order on FMM accuracy, up to a plateau caused by the accumulation of rounding errors. The octree depth was found to have low impact on the accuracy. Validation of the solver is performed through underresolved direct numerical simulation (DNS) of Lamb-Oseen vortex, vortex ring, and colliding vortex ring test cases. The impact of FMM on particle velocities and positions throughout simulations is measured, and key flow diagnostics are provided, indicating minimal FMM impact on the physical validity of simulations.
More chaotic flows exhibited an unbounded nature of FMM error growth while low Reynolds number flows counteracted the FMM error. The performance of the main operations of the solver was profiled, highlighting trade-offs between speed and accuracy, and indicating areas for future performance improvements.
Mitigating Wall Interference in Transonic Wind Tunnel Testing of Swept Wings
A Numerical Study on Flowfield Correction Using Wall Deformation in the Cryogenic Ludwieg Tube Göttingen
angle, chord length, and Mach number, on wall-induced distortions.
The simulations reveal that vertical tunnel walls introduce significant spanwise pressure gradients, especially at higher sweep angles and larger chord lengths, i.e., aspect ratios. These effects are mitigated through a mesh deformation approach based on Radial Basis Functions, which enables the adaptive reshaping of tunnel walls to align with streamlines from an idealized, unbounded flowfield. The implementation of these deformed geometries resulted in substantial improvements in spanwise flow uniformity, reducing the root mean square errors in the pressure coefficient distribution by nearly 50% in critical test section regions. Not only is it possible to reduce spanwise gradients in the flowfield, but also to reduce the difference to infinitely swept conditions almost over the entire width of the test section.
Beyond identifying optimal strategies to reduce the influence of the walls on the flowfield, the thesis validates its numerical findings against existing experimental and numerical data. The proposed methodology offers a valuable toolset for pre-test planning and supports the development of more representative aerodynamic experiments, especially in the context of laminar-to-turbulent transition studies. These contributions provide a scientifically robust foundation for minimizing wall interference in transonic testing and support the advancement of research on laminar-to-turbulent transition. ...
angle, chord length, and Mach number, on wall-induced distortions.
The simulations reveal that vertical tunnel walls introduce significant spanwise pressure gradients, especially at higher sweep angles and larger chord lengths, i.e., aspect ratios. These effects are mitigated through a mesh deformation approach based on Radial Basis Functions, which enables the adaptive reshaping of tunnel walls to align with streamlines from an idealized, unbounded flowfield. The implementation of these deformed geometries resulted in substantial improvements in spanwise flow uniformity, reducing the root mean square errors in the pressure coefficient distribution by nearly 50% in critical test section regions. Not only is it possible to reduce spanwise gradients in the flowfield, but also to reduce the difference to infinitely swept conditions almost over the entire width of the test section.
Beyond identifying optimal strategies to reduce the influence of the walls on the flowfield, the thesis validates its numerical findings against existing experimental and numerical data. The proposed methodology offers a valuable toolset for pre-test planning and supports the development of more representative aerodynamic experiments, especially in the context of laminar-to-turbulent transition studies. These contributions provide a scientifically robust foundation for minimizing wall interference in transonic testing and support the advancement of research on laminar-to-turbulent transition.
Numerical Modeling of Floater Dynamics of a FOWT
For Wind Tunnel Hardware-in-the-Loop Testing
Towards Generative AI-powered Engineering of Critical Systems
Reverse Engineering Tool for Knowledge Based Engineering Applications & Ideation Matrix for AI-powered Automation Systems
Wind assisted ship propulsion: A rotating cylinder study
Design, realisation and characterisation of an aerodynamic rotating cylinder experiment
To accommodate aerodynamic rotating cylinder research at the Low Speed Laboratory of the TU Delft, this study presents the design, realisation and characterisation of an experimental two-dimensional rotating cylinder setup for the SLT wind tunnel facility. Additionally, the effects of testing at a high blockage ratio were investigated for this initial study using the new setup. As a result, the area model blockage ratio deliberately reached an unconventional high 33%, where an aspect ratio of 4.5 was chosen, comparable to full scale WASP applications. The aerodynamic characteristics for three test cases at subcritical Reynolds numbers equal to 62500, 125000 and 250000 with spin ratio ranges equal to 0 ≤ k ≤ 8, 0 ≤ k ≤ 4 and 0 ≤ k ≤ 2 respectively, were obtained by the utilisation of force measurements, particle image velocimetry flow visualisation and proper orthogonal decomposition techniques.
As with similar rotating cylinder experiments, the magnitudes of the presented force coefficients differ in comparison, owing to the large blockage ratio and variations in experimental setup, however the experimental trends in the force coefficient curves are fully captured up to spin ratios of 2.5. Between 0 ≤ k ≤ 0.8, the aerodynamic characteristics are affected by both the Reynolds number and spin ratio, where differences in boundary layer transition, laminar separation bubble formation, boundary layer lengths and vortex shedding behaviour are the underlying mechanisms causing a change in the obtained force coefficients. Transition effects are stronger at the higher subcritical Reynolds numbers, where reversal of the Magnus effect can occur within this range of spin ratios and Reynolds numbers. Beyond k > 0.8, advancing side boundary layer transition has taken place for all tested Reynolds numbers. The force coefficients and flow field topology showed great similarities between the different Reynolds numbers with a further increase of the spin ratio. Slight variations in turbulent kinetic energy production were observed in the retreating side boundary layer and shear layer behaviour, possibly owing to laminar to turbulent transition. For k > 2.0, the periodic shedding of vortical structures is no longer observed, which coincides with the formation of the highly turbulent rotating boundary layer, settling of the near-wake, and the knee in the force coefficient curves within the range of 2.2 < k < 2.6. For remainder of the spin ratios, k > 2.6, the flow field has completely reversed and is pointed in opposite direction of the incoming free stream, where large negative mean drag coefficients and instantaneous force fluctuations are recorded. This is believed to be the result of unsteady nozzle-model gap interactions with the separated region of the cylinder and is dictated by the large blockage ratio.
...
To accommodate aerodynamic rotating cylinder research at the Low Speed Laboratory of the TU Delft, this study presents the design, realisation and characterisation of an experimental two-dimensional rotating cylinder setup for the SLT wind tunnel facility. Additionally, the effects of testing at a high blockage ratio were investigated for this initial study using the new setup. As a result, the area model blockage ratio deliberately reached an unconventional high 33%, where an aspect ratio of 4.5 was chosen, comparable to full scale WASP applications. The aerodynamic characteristics for three test cases at subcritical Reynolds numbers equal to 62500, 125000 and 250000 with spin ratio ranges equal to 0 ≤ k ≤ 8, 0 ≤ k ≤ 4 and 0 ≤ k ≤ 2 respectively, were obtained by the utilisation of force measurements, particle image velocimetry flow visualisation and proper orthogonal decomposition techniques.
As with similar rotating cylinder experiments, the magnitudes of the presented force coefficients differ in comparison, owing to the large blockage ratio and variations in experimental setup, however the experimental trends in the force coefficient curves are fully captured up to spin ratios of 2.5. Between 0 ≤ k ≤ 0.8, the aerodynamic characteristics are affected by both the Reynolds number and spin ratio, where differences in boundary layer transition, laminar separation bubble formation, boundary layer lengths and vortex shedding behaviour are the underlying mechanisms causing a change in the obtained force coefficients. Transition effects are stronger at the higher subcritical Reynolds numbers, where reversal of the Magnus effect can occur within this range of spin ratios and Reynolds numbers. Beyond k > 0.8, advancing side boundary layer transition has taken place for all tested Reynolds numbers. The force coefficients and flow field topology showed great similarities between the different Reynolds numbers with a further increase of the spin ratio. Slight variations in turbulent kinetic energy production were observed in the retreating side boundary layer and shear layer behaviour, possibly owing to laminar to turbulent transition. For k > 2.0, the periodic shedding of vortical structures is no longer observed, which coincides with the formation of the highly turbulent rotating boundary layer, settling of the near-wake, and the knee in the force coefficient curves within the range of 2.2 < k < 2.6. For remainder of the spin ratios, k > 2.6, the flow field has completely reversed and is pointed in opposite direction of the incoming free stream, where large negative mean drag coefficients and instantaneous force fluctuations are recorded. This is believed to be the result of unsteady nozzle-model gap interactions with the separated region of the cylinder and is dictated by the large blockage ratio.
This research implements the Delft Laminar Hump on the vertical stabilizer of subsonic transport aircraft by modeling the effect of the hump as a shift in transition location. By using a Quasi-3D aerodynamic analysis in combination with a transition location database, the effect of the hump on the lift and drag coefficient of the vertical stabilizer is analyzed. The transition location database is constructed by using the external velocity of airfoil sections of the vertical tailplane and the boundary layer solver and stability analysis developed by the Group of Flow Control and Stability within the Delft University of Technology. With this, the N-factor curves along the chord can be calculated. Knowing the respective N-factors of the clean and hump configuration, the associated transition locations can be determined, which are then used to calculate the lift and drag coefficients of the vertical tailplane. To evaluate the aerodynamic effect of the hump on the full aircraft directional and lateral stability a stability analysis based on a method by Fokker / Obert is performed and checked against the CS-25 for Large Aeroplanes regulations by European Aviation Safety Authority (EASA).
It was found that the Delft Laminar Hump (DeLaH) on the vertical stabilizer of a subsonic transport aircraft does not affect the vertical tailplane lift curve slope, thus not affecting the stability of the aircraft. In contrast, the vertical tailplane drag coefficient is reduced by the hump. Retrofitting the hump on Airbus A320 (conventional tail) and the Fokker F-28 Mk1000 (T-tail) results in a reduction of the vertical tailplane drag coefficient of 6.73% and 8.72%, respectively. Translating this vertical tail drag reduction to the full aircraft drag coefficient results in a reduction of 0.17% and 0.34%. To evaluate the effect of the hump on weight and fuel consumption, additional weight and mission analyses are performed. Evaluating the harmonic range, an fuel reduction due to the hump of 0.16% and 0.32% is established, for the Airbus A320 and Fokker F-28 Mk1000, respectively. The aircraft weight is reduced by the same percentage through the fuel reduction, as it is assumed that the added weight due to the hump itself is negligible.
Additionally, two sensitivity analyses were performed, namely, sweep angle variation and surface area scaling to analyze the effectiveness of the hump for different vertical tailplane geometries. The effect of sweep angle on hump effectiveness does not affect the vertical tailplane lift curve slope and thus also not the stability coefficients. For the full aircraft drag coefficient, the hump effectiveness has an exponential relation with sweep angle and is most effective at lower sweep angles. A maximum full aircraft drag reduction was found of 0.41% at 30 deg sweep with an equivalent fuel reduction of 0.39%. Overall it is concluded that lower sweep angles are beneficial as the hump is most effective and results in reduced vertical tailplane weight, less fuel weight as well as an increased stability margin. Analyzing the effect of surface area scaling, the hump has no effect on the vertical tailplane lift curve slope regardless of surface area, again retaining the aircraft’s stability. For the full aircraft drag coefficient, the hump effectiveness increases linearly for increasing surface area up to 0.37% at a surface scaling factor of 1.2 times the original vertical tailplane surface area. In terms of fuel reduction, a maximum value of 0.35% was found. There will be an optimal vertical tailplane surface area, since the hump effectiveness increases for increasing surface area, whilst for the full aircraft drag, vertical tailplane weight, and fuel weight a smaller surface area is preferred. The stability margin becomes the limiting factor as a minimum surface area is required for sufficient stability. Comparing the baseline aircraft, the hump is more effective for the Fokker F-28 Mk1000 over the entire range of scaling factors and sweep angles. This leads to the suspicion that taper- and aspect ratio, and cruise speed play an important role in the effectiveness of the hump, but more research is required.
This research shows that the Delft Laminar Hump has a significant drag-reducing effect on the overall aircraft, whilst not affecting the aircraft’s stability. Even though the fuel savings for an individual aircraft are not very large, on a fleet level this would be significant. The hump can be retrofitted on existing aircraft by gluing it on the outer skin, making it a relatively simple and cheap way to improve efficiency for aircraft manufacturers. Nevertheless, more research is required before implementing the hump on commercial aircraft as it is still unknown whether the hump also works on the suction side of the wing as well as whether the hump causes a shock at cruise Mach. Also, interaction effects with the horizontal stabilizer and fuselage need to be taken into account, to fully quantify the effectiveness of the hump. Dedicated wind tunnel experiments, flight tests, and/or CFD simulations are necessary. ...
This research implements the Delft Laminar Hump on the vertical stabilizer of subsonic transport aircraft by modeling the effect of the hump as a shift in transition location. By using a Quasi-3D aerodynamic analysis in combination with a transition location database, the effect of the hump on the lift and drag coefficient of the vertical stabilizer is analyzed. The transition location database is constructed by using the external velocity of airfoil sections of the vertical tailplane and the boundary layer solver and stability analysis developed by the Group of Flow Control and Stability within the Delft University of Technology. With this, the N-factor curves along the chord can be calculated. Knowing the respective N-factors of the clean and hump configuration, the associated transition locations can be determined, which are then used to calculate the lift and drag coefficients of the vertical tailplane. To evaluate the aerodynamic effect of the hump on the full aircraft directional and lateral stability a stability analysis based on a method by Fokker / Obert is performed and checked against the CS-25 for Large Aeroplanes regulations by European Aviation Safety Authority (EASA).
It was found that the Delft Laminar Hump (DeLaH) on the vertical stabilizer of a subsonic transport aircraft does not affect the vertical tailplane lift curve slope, thus not affecting the stability of the aircraft. In contrast, the vertical tailplane drag coefficient is reduced by the hump. Retrofitting the hump on Airbus A320 (conventional tail) and the Fokker F-28 Mk1000 (T-tail) results in a reduction of the vertical tailplane drag coefficient of 6.73% and 8.72%, respectively. Translating this vertical tail drag reduction to the full aircraft drag coefficient results in a reduction of 0.17% and 0.34%. To evaluate the effect of the hump on weight and fuel consumption, additional weight and mission analyses are performed. Evaluating the harmonic range, an fuel reduction due to the hump of 0.16% and 0.32% is established, for the Airbus A320 and Fokker F-28 Mk1000, respectively. The aircraft weight is reduced by the same percentage through the fuel reduction, as it is assumed that the added weight due to the hump itself is negligible.
Additionally, two sensitivity analyses were performed, namely, sweep angle variation and surface area scaling to analyze the effectiveness of the hump for different vertical tailplane geometries. The effect of sweep angle on hump effectiveness does not affect the vertical tailplane lift curve slope and thus also not the stability coefficients. For the full aircraft drag coefficient, the hump effectiveness has an exponential relation with sweep angle and is most effective at lower sweep angles. A maximum full aircraft drag reduction was found of 0.41% at 30 deg sweep with an equivalent fuel reduction of 0.39%. Overall it is concluded that lower sweep angles are beneficial as the hump is most effective and results in reduced vertical tailplane weight, less fuel weight as well as an increased stability margin. Analyzing the effect of surface area scaling, the hump has no effect on the vertical tailplane lift curve slope regardless of surface area, again retaining the aircraft’s stability. For the full aircraft drag coefficient, the hump effectiveness increases linearly for increasing surface area up to 0.37% at a surface scaling factor of 1.2 times the original vertical tailplane surface area. In terms of fuel reduction, a maximum value of 0.35% was found. There will be an optimal vertical tailplane surface area, since the hump effectiveness increases for increasing surface area, whilst for the full aircraft drag, vertical tailplane weight, and fuel weight a smaller surface area is preferred. The stability margin becomes the limiting factor as a minimum surface area is required for sufficient stability. Comparing the baseline aircraft, the hump is more effective for the Fokker F-28 Mk1000 over the entire range of scaling factors and sweep angles. This leads to the suspicion that taper- and aspect ratio, and cruise speed play an important role in the effectiveness of the hump, but more research is required.
This research shows that the Delft Laminar Hump has a significant drag-reducing effect on the overall aircraft, whilst not affecting the aircraft’s stability. Even though the fuel savings for an individual aircraft are not very large, on a fleet level this would be significant. The hump can be retrofitted on existing aircraft by gluing it on the outer skin, making it a relatively simple and cheap way to improve efficiency for aircraft manufacturers. Nevertheless, more research is required before implementing the hump on commercial aircraft as it is still unknown whether the hump also works on the suction side of the wing as well as whether the hump causes a shock at cruise Mach. Also, interaction effects with the horizontal stabilizer and fuselage need to be taken into account, to fully quantify the effectiveness of the hump. Dedicated wind tunnel experiments, flight tests, and/or CFD simulations are necessary.
At the moderate chord Reynolds numbers relevant here, laminar–turbulent transition, boundary layer separation and the formation or suppression of LSBs can alter lift, drag, stall margins and noise. LSBs arise when a laminar layer separates, transitions within a free shear layer and then reattaches, resulting in a turbulent flow. A propeller modifies this flow field by generating a non-uniform, unsteady slipstream consisting of accelerated axial flow, swirl, and a helical system of tip and root vortices and blade wakes. The resulting spatially and temporally varying inflow alters local incidence, dynamic pressure and boundary layer dynamics over the wing. Existing studies rely primarily on time-averaged measurements and lack sufficient spatial and temporal resolution near the wall. As a result, the detailed mechanisms by which helical vortices and wake sheets interact with the downstream boundary layer, their spanwise variation within and around the slipstream core, and their influence on LSB dynamics remain only partially understood.
The present thesis aims to provide an experimental characterisation of how a propeller slipstream modifies a downstream laminar boundary layer behaviour. Two complementary campaigns have been used to answer the research objective: oil-flow visualisations and acoustic measurements on the surface of an airfoil placed under a propeller slipstream to understand the time-averaged boundary layer in a global sense, and a local, high-resolution investigation using phase-locked stereoscopic Particle Image Velocimetry (sPIV) to resolve the vortex structures within the slipstream and understand their effect on the boundary layer. Together, these experiments address the questions of (i) how the slipstream alters laminar–turbulent transition and LSB formation, and (ii) what role unsteady vortical structures within the slipstream play in triggering and modulating transition along the span.
The results show that the propeller slipstream strongly energises the downstream boundary layer and generally promotes earlier transition, but in a manner that is highly non-uniform in both span and blade-passage phase. The results indicate that under a propeller slipstream, transition is advanced and the boundary layer thickens on the inboard side, where inboard shearing and higher slipstream velocities amplify near-wall turbulence. The slipstream also modifies LSB behaviour, and depending upon slipstream amplitude and effective local incidence angle, the LSB may be suppressed entirely, shortened and displaced upstream, or persist within regions of weaker propeller loading. Phase-locked sPIV reveals that these behaviours are governed by an intrinsically three-dimensional, intermittent interaction between the boundary layer and a coupled system of primary tip vortices, secondary wall-originating vortices and blade wakes. Wake-impingement events generate short bursts of high shear and TKE separated by phases of weakly turbulent or nearly laminar near-wall flow. Comparable TKE levels for tripped and untripped cases at the same wall-normal position show that near-wall turbulence inside the slipstream is dominated by the imposed unsteady forcing rather than by the state of the boundary layer. ...
At the moderate chord Reynolds numbers relevant here, laminar–turbulent transition, boundary layer separation and the formation or suppression of LSBs can alter lift, drag, stall margins and noise. LSBs arise when a laminar layer separates, transitions within a free shear layer and then reattaches, resulting in a turbulent flow. A propeller modifies this flow field by generating a non-uniform, unsteady slipstream consisting of accelerated axial flow, swirl, and a helical system of tip and root vortices and blade wakes. The resulting spatially and temporally varying inflow alters local incidence, dynamic pressure and boundary layer dynamics over the wing. Existing studies rely primarily on time-averaged measurements and lack sufficient spatial and temporal resolution near the wall. As a result, the detailed mechanisms by which helical vortices and wake sheets interact with the downstream boundary layer, their spanwise variation within and around the slipstream core, and their influence on LSB dynamics remain only partially understood.
The present thesis aims to provide an experimental characterisation of how a propeller slipstream modifies a downstream laminar boundary layer behaviour. Two complementary campaigns have been used to answer the research objective: oil-flow visualisations and acoustic measurements on the surface of an airfoil placed under a propeller slipstream to understand the time-averaged boundary layer in a global sense, and a local, high-resolution investigation using phase-locked stereoscopic Particle Image Velocimetry (sPIV) to resolve the vortex structures within the slipstream and understand their effect on the boundary layer. Together, these experiments address the questions of (i) how the slipstream alters laminar–turbulent transition and LSB formation, and (ii) what role unsteady vortical structures within the slipstream play in triggering and modulating transition along the span.
The results show that the propeller slipstream strongly energises the downstream boundary layer and generally promotes earlier transition, but in a manner that is highly non-uniform in both span and blade-passage phase. The results indicate that under a propeller slipstream, transition is advanced and the boundary layer thickens on the inboard side, where inboard shearing and higher slipstream velocities amplify near-wall turbulence. The slipstream also modifies LSB behaviour, and depending upon slipstream amplitude and effective local incidence angle, the LSB may be suppressed entirely, shortened and displaced upstream, or persist within regions of weaker propeller loading. Phase-locked sPIV reveals that these behaviours are governed by an intrinsically three-dimensional, intermittent interaction between the boundary layer and a coupled system of primary tip vortices, secondary wall-originating vortices and blade wakes. Wake-impingement events generate short bursts of high shear and TKE separated by phases of weakly turbulent or nearly laminar near-wall flow. Comparable TKE levels for tripped and untripped cases at the same wall-normal position show that near-wall turbulence inside the slipstream is dominated by the imposed unsteady forcing rather than by the state of the boundary layer.
Toward an End-to-End Pipeline from Requirements to Code
Large Language Model Supported Coding Assistant for Knowlegde Based Engineering Application Development
This research validates that retrieval-augmented approaches offer a practical alternative to retraining models for specialized domains with limited data, such as ParaPy. In these approaches, AI systems dynamically access domain-specific knowledge during operation rather than relying solely on their training. This has significant implications for industries or institutions using proprietary tools where comprehensive model retraining is economically infeasible.
The research implements this approach by developing and evaluating a dual-agent framework for AI-assisted KBE application development that operates within industrial privacy and security constraints. The framework comprises a Developer Agent optimized for code generation and debugging with the ParaPy SDK, and an Educational Agent focused on ParaPy learning support and documentation. Both agents access a knowledge infrastructure that uses semantic search over indexed ParaPy documentation, curated examples, and technical references. Additionally, the Developer Agent employs verification mechanisms that progressively check code at two core levels: syntax correctness (ensuring the code follows programming language rules) and successful execution (confirming the code runs without errors).
User testing revealed how different skill levels benefit from AI assistance. Intermediate users benefited most, showing dramatic improvements in productivity and performance. Novice users achieved substantial productivity gains and reduced framework-specific (ParaPy) errors significantly, with task completion rates approaching expert baseline performance. Expert users, however, experienced slight performance degradation due to reduced code review under time pressure. The framework successfully reduced knowledge barriers for novice and intermediate users, broadening access to specialized engineering tools.
Despite these successes, the framework has persistent limitations in understanding three-dimensional spatial relationships. This is critical for KBE applications where code must define the precise position, orientation, and assembly of physical components. The framework struggles to correctly place components in space or apply proper rotational transformations. This produces code that may be syntactically correct but results in misaligned parts or incorrectly oriented features. These geometric errors require iterative refinement with human guidance, representing a fundamental limitation of the current approach and language model architectures.
While geometric reasoning limitations suggest fundamental boundaries of current AI capabilities, the demonstrated productivity improvements and reduced knowledge requirements establish a foundation for broader AI adoption in knowledge-intensive engineering domains. The framework contributes a validated operational prototype that addresses critical gaps in AI-assisted KBE development: reducing the manual coding bottleneck, lowering knowledge barriers for new users, and providing privacy-compliant deployment options. The framework functions most effectively as a development accelerator requiring expert oversight, supporting human engineers rather than replacing them.
Keywords: Knowledge-Based Engineering, Large Language Models, Code Generation, ParaPy, Retrieval-Augmented Generation, AI-Assisted Development, Aerospace Engineering, Multi-Agent Systems ...
This research validates that retrieval-augmented approaches offer a practical alternative to retraining models for specialized domains with limited data, such as ParaPy. In these approaches, AI systems dynamically access domain-specific knowledge during operation rather than relying solely on their training. This has significant implications for industries or institutions using proprietary tools where comprehensive model retraining is economically infeasible.
The research implements this approach by developing and evaluating a dual-agent framework for AI-assisted KBE application development that operates within industrial privacy and security constraints. The framework comprises a Developer Agent optimized for code generation and debugging with the ParaPy SDK, and an Educational Agent focused on ParaPy learning support and documentation. Both agents access a knowledge infrastructure that uses semantic search over indexed ParaPy documentation, curated examples, and technical references. Additionally, the Developer Agent employs verification mechanisms that progressively check code at two core levels: syntax correctness (ensuring the code follows programming language rules) and successful execution (confirming the code runs without errors).
User testing revealed how different skill levels benefit from AI assistance. Intermediate users benefited most, showing dramatic improvements in productivity and performance. Novice users achieved substantial productivity gains and reduced framework-specific (ParaPy) errors significantly, with task completion rates approaching expert baseline performance. Expert users, however, experienced slight performance degradation due to reduced code review under time pressure. The framework successfully reduced knowledge barriers for novice and intermediate users, broadening access to specialized engineering tools.
Despite these successes, the framework has persistent limitations in understanding three-dimensional spatial relationships. This is critical for KBE applications where code must define the precise position, orientation, and assembly of physical components. The framework struggles to correctly place components in space or apply proper rotational transformations. This produces code that may be syntactically correct but results in misaligned parts or incorrectly oriented features. These geometric errors require iterative refinement with human guidance, representing a fundamental limitation of the current approach and language model architectures.
While geometric reasoning limitations suggest fundamental boundaries of current AI capabilities, the demonstrated productivity improvements and reduced knowledge requirements establish a foundation for broader AI adoption in knowledge-intensive engineering domains. The framework contributes a validated operational prototype that addresses critical gaps in AI-assisted KBE development: reducing the manual coding bottleneck, lowering knowledge barriers for new users, and providing privacy-compliant deployment options. The framework functions most effectively as a development accelerator requiring expert oversight, supporting human engineers rather than replacing them.
Keywords: Knowledge-Based Engineering, Large Language Models, Code Generation, ParaPy, Retrieval-Augmented Generation, AI-Assisted Development, Aerospace Engineering, Multi-Agent Systems
Effect of Large scale Turbulence on Propeller Aerodynamic and Aeroacoustic performance
An Experimental Investigation
characteristics, local windspeed variations, etc.. Unlike the well-documented effects of aerial vehicles flying under steady freestream or small-scale turbulence impingement, research on their performance when subjected to large-scale turbulence representative of an urban airspace is relatively scanty. This experimental work aims to generate large scale turbulence in the order of the rotor diameter and analyze its influence on propeller loading and noise emission.
Bluff body shedding from a cylinder is utilized to generate rotor scale turbulence in the inflow, with a variation in upstream cylinder placement tested to quantify the influence of it’s proximity to the propeller. The presence of an upstream obstruction results in severe penalties to the aerodynamic performance and thrust generation compared to an isolated propeller. An increase in rotor scale fluctuations in the inflow leads to an increased intensity of low-frequency loading fluctuations. The highly turbulent inflow has a severe impact on the noise emissions, with an overall increase in the broadband content and retention of discrete tones emitted at BPF (blade passing frequency) harmonics across all tested advance ratios; contrasting drastically with the emission of the isolated propeller. Further, with the cylinder obstruction placed closer to the propeller, the effect of haystacking is observed in the noise emissions, which dominates the high-frequency range and results in a spectrum comprising of purely broadband content above the 2nd
harmonic of the BPF. The findings highlight a strong influence of large-scale turbulence on propeller performance and noise emissions, while emphasizing the requirement for further investigation which isolates and analyzes each underlying effect to obtain a complete understanding of the identified influence. ...
characteristics, local windspeed variations, etc.. Unlike the well-documented effects of aerial vehicles flying under steady freestream or small-scale turbulence impingement, research on their performance when subjected to large-scale turbulence representative of an urban airspace is relatively scanty. This experimental work aims to generate large scale turbulence in the order of the rotor diameter and analyze its influence on propeller loading and noise emission.
Bluff body shedding from a cylinder is utilized to generate rotor scale turbulence in the inflow, with a variation in upstream cylinder placement tested to quantify the influence of it’s proximity to the propeller. The presence of an upstream obstruction results in severe penalties to the aerodynamic performance and thrust generation compared to an isolated propeller. An increase in rotor scale fluctuations in the inflow leads to an increased intensity of low-frequency loading fluctuations. The highly turbulent inflow has a severe impact on the noise emissions, with an overall increase in the broadband content and retention of discrete tones emitted at BPF (blade passing frequency) harmonics across all tested advance ratios; contrasting drastically with the emission of the isolated propeller. Further, with the cylinder obstruction placed closer to the propeller, the effect of haystacking is observed in the noise emissions, which dominates the high-frequency range and results in a spectrum comprising of purely broadband content above the 2nd
harmonic of the BPF. The findings highlight a strong influence of large-scale turbulence on propeller performance and noise emissions, while emphasizing the requirement for further investigation which isolates and analyzes each underlying effect to obtain a complete understanding of the identified influence.
Development of a Cessna Skymaster mathematical model
A Two Step method aerodynamic and engine model identification from flight test data
Related dataset 4TU.ResearchData:
https://doi.org/10.4121/a74d4324-ce07-45a9-9e9a-d4177e733a0b ...
Related dataset 4TU.ResearchData:
https://doi.org/10.4121/a74d4324-ce07-45a9-9e9a-d4177e733a0b
262,000 and at angles of attack comprised between 1 and 5 degrees, in 1 degree increments. Two different piezofoil designs are used, ”in-line”, spanning most of the airfoil chord and ”staggered”, shorter but with an improved spatial resolution. Complementary measurements are performed using surface hot wire anemometry, oil flow visualization, and surface pressure taps to provide a comprehensive characterization of both mean and fluctuating flow features.
The primary objective of the study is to relate the surface pressure fluctuations within the LSB to its dynamic phenomena, specifically, shear-layer flapping and vortex shedding, and to identify the optimal sensor placement for their detection. The existence and the characteristics of the laminar separation bubbles at the range of Reynolds number and angles of attack considered is confirmed through surface pressure measurements using pressure transducers and oil flow visualization. Analysis of the spectra and of the standard deviation in the separation and reattachment regions demonstrates that the piezofoil sensor successfully detects and accurately resolves vortex shedding, but is unable to capture the low-frequency flapping motion. The cross correlation analysis provided further insight into the vortex shedding process, enabling the estimation of the convective velocity and streamwise wavelength of the vortical structures. Heating of the piezofoil and appropriate signal filtering are found to be effective in enhancing the signal-to-noise ratio and mitigating electromagnetic interference effects. ...
262,000 and at angles of attack comprised between 1 and 5 degrees, in 1 degree increments. Two different piezofoil designs are used, ”in-line”, spanning most of the airfoil chord and ”staggered”, shorter but with an improved spatial resolution. Complementary measurements are performed using surface hot wire anemometry, oil flow visualization, and surface pressure taps to provide a comprehensive characterization of both mean and fluctuating flow features.
The primary objective of the study is to relate the surface pressure fluctuations within the LSB to its dynamic phenomena, specifically, shear-layer flapping and vortex shedding, and to identify the optimal sensor placement for their detection. The existence and the characteristics of the laminar separation bubbles at the range of Reynolds number and angles of attack considered is confirmed through surface pressure measurements using pressure transducers and oil flow visualization. Analysis of the spectra and of the standard deviation in the separation and reattachment regions demonstrates that the piezofoil sensor successfully detects and accurately resolves vortex shedding, but is unable to capture the low-frequency flapping motion. The cross correlation analysis provided further insight into the vortex shedding process, enabling the estimation of the convective velocity and streamwise wavelength of the vortical structures. Heating of the piezofoil and appropriate signal filtering are found to be effective in enhancing the signal-to-noise ratio and mitigating electromagnetic interference effects.
By the end of the thesis, it was concluded that although slotted winglets reduced induced drag, they led to a significant increase in profile drag, resulting in higher overall drag compared to unslotted winglets. Additionally, the slots caused a loss in lift. The overall aerodynamic performance, measured by the lift-to-drag ratio, was also higher for the
unslotted winglet. Among the slotted winglets, static bending was common, while wingtip vibrations were minimal. The most flexible slotted winglet had the lowest induced drag. However, the results indicate that at very low Reynolds numbers, slotted winglets deteriorate the wing’s aerodynamic performance compared to unslotted ones. Among the slotted winglets, those with intermediate flexibility demonstrated the best aerodynamic performance, highlighting the importance of optimizing wingtip flexibility. ...
By the end of the thesis, it was concluded that although slotted winglets reduced induced drag, they led to a significant increase in profile drag, resulting in higher overall drag compared to unslotted winglets. Additionally, the slots caused a loss in lift. The overall aerodynamic performance, measured by the lift-to-drag ratio, was also higher for the
unslotted winglet. Among the slotted winglets, static bending was common, while wingtip vibrations were minimal. The most flexible slotted winglet had the lowest induced drag. However, the results indicate that at very low Reynolds numbers, slotted winglets deteriorate the wing’s aerodynamic performance compared to unslotted ones. Among the slotted winglets, those with intermediate flexibility demonstrated the best aerodynamic performance, highlighting the importance of optimizing wingtip flexibility.
Battery Pack Thermal Modeling for Electric Aircraft
A Case Study
The electronic equivalent circuit model, used to simulate voltage characteristics and heat production in a single lithium ion battery cell, requires pulse current characterization tests for accurate parameter estimation.
Extensive testing has been conducted to gather these data. The model achieves accurate voltage modeling accuracy with a low root mean square error Adding more than one RC branch to the circuit did not significantly improve the accuracy of the model.
The electronic equivalent circuit and lumped parameter thermal network models were validated with two flight data sets. Both ribbon and cold plate cooling solutions effectively matched the validation temperatures, performing similarly. In contrast, the air cooling solution was less effective. In case of ribbon cooling, the maximum cell temperature was highly sensitive to its geometric parameters, specifically the angle and height of the ribbon. The sensitivity of the cold plate solution in terms of maximum battery temperature was influenced by the diameter of the cooling channel and the thickness of the plate. The air cooling showed sensitivity in terms of maximum battery temperature relative to the inter-cell gap width. For the ribbon model, varying the number of thermal nodes led to a convergence in the maximum battery temperature as the node count increased.
Using the validated ribbon cooling model, two operational scenarios were analyzed. The first scenario involved charging operations, where simulations closely matched temperature validation data, showing only a minor temperature rise in the battery pack. The second scenario tested cold weather operations with ambient temperatures reduced to approximately 0 ◦C. Here, two simulations were conducted: one with the battery preheated to 20 ◦C and another without preheating. Without preheating, the battery pack’s temperature neared the operational lower limit of 0 ◦C. Preheating prevented reaching this lower limit. It is recommended to preheat the battery pack using an external charger, as using the battery’s own energy for preheating is inefficient.
The thesis was concluded by using the developed modeling approach to size and model a battery pack for the Eviation Alice, a larger aircraft. The approach was successfully scaled to this large use case with a known power profile. Furthermore, due to significant ambient temperature effects and higher operational altitudes compared to the Pipistrel Velis Electro, thermal insulation will be necessary for the battery pack to maintain temperatures above the lower operational limit of 0 ◦C during typical missions. ...
The electronic equivalent circuit model, used to simulate voltage characteristics and heat production in a single lithium ion battery cell, requires pulse current characterization tests for accurate parameter estimation.
Extensive testing has been conducted to gather these data. The model achieves accurate voltage modeling accuracy with a low root mean square error Adding more than one RC branch to the circuit did not significantly improve the accuracy of the model.
The electronic equivalent circuit and lumped parameter thermal network models were validated with two flight data sets. Both ribbon and cold plate cooling solutions effectively matched the validation temperatures, performing similarly. In contrast, the air cooling solution was less effective. In case of ribbon cooling, the maximum cell temperature was highly sensitive to its geometric parameters, specifically the angle and height of the ribbon. The sensitivity of the cold plate solution in terms of maximum battery temperature was influenced by the diameter of the cooling channel and the thickness of the plate. The air cooling showed sensitivity in terms of maximum battery temperature relative to the inter-cell gap width. For the ribbon model, varying the number of thermal nodes led to a convergence in the maximum battery temperature as the node count increased.
Using the validated ribbon cooling model, two operational scenarios were analyzed. The first scenario involved charging operations, where simulations closely matched temperature validation data, showing only a minor temperature rise in the battery pack. The second scenario tested cold weather operations with ambient temperatures reduced to approximately 0 ◦C. Here, two simulations were conducted: one with the battery preheated to 20 ◦C and another without preheating. Without preheating, the battery pack’s temperature neared the operational lower limit of 0 ◦C. Preheating prevented reaching this lower limit. It is recommended to preheat the battery pack using an external charger, as using the battery’s own energy for preheating is inefficient.
The thesis was concluded by using the developed modeling approach to size and model a battery pack for the Eviation Alice, a larger aircraft. The approach was successfully scaled to this large use case with a known power profile. Furthermore, due to significant ambient temperature effects and higher operational altitudes compared to the Pipistrel Velis Electro, thermal insulation will be necessary for the battery pack to maintain temperatures above the lower operational limit of 0 ◦C during typical missions.
Vertical Axis Wind Turbine Optimization for Ship Propulsion
Using a free wake vortex model
From the wind tunnel experiments, it was found that split flaps on the outboard wing section can effectively increase the directional control power over angles of attack between 0 and 30 degrees. However, yaw control is lost when over negative angles of attack due to lower wing stall. The maximum decrease in split flap effectiveness over positive angles of attack is found around 17.5 degrees, where a leading edge vortex is present over the outboard wing. This decreases pressure over the upper split flap, resulting in a effectiveness decrease of around 41%. As the effectiveness does not decrease further, split flaps can be continuously effective at higher angles of attack when compared to the winglet rudders. The low pressure on the upper flap also causes large adverse coupled moments in pitch and roll. The effect of split flaps on the yawing moment is found to be linear with deflection angle, where their effect on other aerodynamic properties is found to be more non-linear.
The deflection of outboard split flaps do not have a significant interference effect on rudder yaw power, but can have some interference effects on adjacent main wing control surfaces. Differential deflection between the upper and lower flap has been shown to potentially decrease coupling in pitch and roll. The split flaps can also be globally rotated trailing edge down to mitigate adverse coupled moments while beneficially increasing the total created yaw.
From trim calculations, it was found that a maximum additional yaw coefficient of 2.4113e-3 has to be provided by the split flaps. Designs with a maximum deflection angle above 30 degrees are deemed feasible, as this would maximally require only the replacement of the current CS3 surfaces. When a maximum deflection of 60 degrees is set by the designer, a sub-scale split flap width of 111.87 mm is needed, which translates to a full-scale split flap of 2.431 m. Based on the sensitivity analysis and projected Reynolds effects, this is considered a conservative design for the full-scale Flying V. At 0 degrees angle of attack, the recommended geometry is projected to increase the maximum directional control power of the Flying V by 38.1%. At 27.5 degrees, the maximum directional control power can even be increased by 85.5%. Both increases come at the cost of a significant drag penalty.
...
From the wind tunnel experiments, it was found that split flaps on the outboard wing section can effectively increase the directional control power over angles of attack between 0 and 30 degrees. However, yaw control is lost when over negative angles of attack due to lower wing stall. The maximum decrease in split flap effectiveness over positive angles of attack is found around 17.5 degrees, where a leading edge vortex is present over the outboard wing. This decreases pressure over the upper split flap, resulting in a effectiveness decrease of around 41%. As the effectiveness does not decrease further, split flaps can be continuously effective at higher angles of attack when compared to the winglet rudders. The low pressure on the upper flap also causes large adverse coupled moments in pitch and roll. The effect of split flaps on the yawing moment is found to be linear with deflection angle, where their effect on other aerodynamic properties is found to be more non-linear.
The deflection of outboard split flaps do not have a significant interference effect on rudder yaw power, but can have some interference effects on adjacent main wing control surfaces. Differential deflection between the upper and lower flap has been shown to potentially decrease coupling in pitch and roll. The split flaps can also be globally rotated trailing edge down to mitigate adverse coupled moments while beneficially increasing the total created yaw.
From trim calculations, it was found that a maximum additional yaw coefficient of 2.4113e-3 has to be provided by the split flaps. Designs with a maximum deflection angle above 30 degrees are deemed feasible, as this would maximally require only the replacement of the current CS3 surfaces. When a maximum deflection of 60 degrees is set by the designer, a sub-scale split flap width of 111.87 mm is needed, which translates to a full-scale split flap of 2.431 m. Based on the sensitivity analysis and projected Reynolds effects, this is considered a conservative design for the full-scale Flying V. At 0 degrees angle of attack, the recommended geometry is projected to increase the maximum directional control power of the Flying V by 38.1%. At 27.5 degrees, the maximum directional control power can even be increased by 85.5%. Both increases come at the cost of a significant drag penalty.