Rene Steijl

• University of Glasgow

As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably test their algorithms on real quantum hardware, which is still too limited. Instead, quantum computing simulat...

This work proposes an extended version of the quantum-kinetic chemistry models, aiming to accurately reproduce experimental measurements and high-fidelity calculations in both thermal equilibrium and non-equilibrium. The extension involves the development of new formulations, incorporating a set of tunable parameters obtained from a non-linear leas...

This work presents a new formulation of the quantum-kinetic (QK) chemistry models, in which the vibrational excitation is modeled with an anharmonic oscillator model. The new formulations are applied to some of the most representative dissociation reactions occurring during an Earth re-entry. The newly derived analytical expressions are implemented...

This article introduces a novel model for describing the electronic excited states in the direct simulation Monte Carlo (DSMC) technique. The model involves the coupling the vibrational and electronic modes of molecular species, enabling each electronic excited state to excite its unique vibrational quantum levels. Numerical techniques are develope...

This work investigates the ability of the partially averaged Navier-Stokes (PANS) method to accurately predict self-sustained shock oscillations, also known as transonic buffet, on a supercritical aerofoil at high Reynolds numbers. Attention is paid to the comparison with unsteady Reynolds-averaged Navier Stokes (URANS) results to show the benefits...

Implementation of floating-point arithmetic with consistent rounding is a critical component of many quantum algorithms. Quantum circuit implementations for squaring and division serve as examples here. This work was motivated by ongoing work in developing quantum algorithms for scientific and engineering computing applications, where this type of...

An extension to the normal shock relations for a thermally perfect, calorically imperfect gas, modelling the vibrational excitation with an anharmonic oscillator model and including the influence of electronic modes, is derived and studied. Such additional considerations constitute an extension to the work achieved in the past, which modelled the c...

At hypersonic speeds, vehicles are subjected to extreme aerothermodynamic conditions, which require accurate pre-dictions of the internal degrees of freedom of molecules. The harmonic oscillator (HO) model is commonly used to model the vibrational excitation of molecules in the framework of direct simulation Monte Carlo. Although it benefits from a...

We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.

We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equ...

A novel version of the Quantum-Kinetic (QK) chemistry models where the vibrational energy is treated with an anharmonic oscillator model (aHO) and the colliding partner regarded as a reactive species is investigated for the dissociation of oxygen. The dissociation reaction rates are validated for adiabatic reactor simulations in thermal equilibrium...

As quantum computing technology continues to develop, the need for research into novel quantum algorithms is growing. However, such algorithms cannot yet be reliably tested on actual quantum hardware, which is still limited in several ways, including qubit coherence times, connectivity, and available qubits. To facilitate the development of novel a...

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the equations of flui...

The application of Quantum Computing (QC) to fluid dynamics simulation has developed into a dynamic research topic in recent years. With many flow problems of scientific and engineering interest requiring large computational resources, the potential of QC to speed-up simulations and facilitate more detailed modeling forms the main motivation for th...

Vehicles undergoing hypersonic speed experience extreme aerothermodynamic conditions. Real gas effects cannot be neglected, and thus internal degrees of freedom of molecules being partially/fully excited must be carefully predicted in order to accurately capture the physics of the flowfield. Within direct simulation Monte Carlo solvers, a harmonic...

A parametric study of multiple shock wave boundary layer interactions is presented in this paper. All results were obtained using the computational fluid dynamics solver of Glasgow University. Such interactions often occur in high-speed intakes, depending on the state of the upstream boundary layer, and can adversely affect the performance of the i...

Among the many computational models for quantum computing, the Quantum Circuit Model is the most well-known and used model for interacting with current quantum hardware. The practical implementation of quantum computers is a very active research field. Despite this progress, access to physical quantum computers remains relatively limited. Furthermo...

For efficient hardware-accelerated simulations of quantum circuits, we can define hardware-specific quantum-circuit transformations. We use a functional programming approach to create a quantum-circuit analysis and transformation method implemented in Haskell. This tool forms a key part of our larger quantum-computing simulation toolchain. As an ex...

In this work, computational fluid dynamics was used to support safety analyses of rotors operating in ground effect. Initially, the research focused on the evaluation and prediction of the outwash generated by a hovering micro-rotor, and time-averaged outflow velocities were compared with experimental results. Then, using scaling factors, the simul...

View Video Presentation: https://doi.org/10.2514/6.2022-1686.vid Predicting the flowfield around a supersonic store at a high incidence angle is challenging due to the presence of vortices and shocks that interact with each other. The complexity of the problem is further increased by the presence of wing-body and wing-tail junctions giving rise to...

Computational fluid dynamics (CFD) is used here to predict the behaviour of ground particles, uplifted by a two-bladed rotor. The main focus is to define a safety area where the presence of particles can be considered safe, and compare this area with other distance based criteria. Using data of three different aircraft, scaling factors have been us...

View Video Presentation: https://doi.org/10.2514/6.2021-2625.vid In this work, computational fluid dynamics is used to perform safety analyses of rotors operating in ground effect. Initially, the paper focuses on the evaluation and prediction of the outwash generated by a micro-rotor operating at different heights above the ground. Time-averaged ou...

The flow of high-speed air in ducts may result in the occurrence of multiple shock-wave/boundary-layer interactions. Understanding the consequences of such interactions, which may include distortion of the velocity field, enhanced turbulence production, and flow separation, is of great importance in understanding the operating limits and performanc...

Shock wave boundary layer interactions occur in many aerospace applications, and of particular interest are the interactions occurring in high-speed intakes. The high-speed intakes aim to decelerate the flow with minimum losses using a series of oblique shocks followed by a weak normal shock. Depending on the state of the boundary layer and on the...

A parametric study of Multiple Shock Wave Boundary Layer Interactions is presented in this paper. All results were obtained using the Computational Fluid Dynamics Solver of Glasgow University.Such interactions often occur in high-speed intakes, depending on the state of the upstream boundary layer, and can adversely affect the performance of the in...

In recent years, significant progress has been made in the development of quantum algorithms for linear ordinary differential equations as well as linear partial differential equations. There has not been similar progress in the development of quantum algorithms for nonlinear differential equations. In the present work, the focus is on nonlinear pa...

Practical applications involve flows that often have more than one constituent. Therefore, the capability to model a gas mixture flow is important. Extending kinetic model equations of the Bhatnagar–Gross–Krook type from a single-species gas to multi-species gas mixtures presents a number of important challenges. This challenge is further pronounce...

A novel quantum algorithm implementing a discrete-velocity method for the collisionless Boltzmann equation is introduced. The algorithm is designed for application on a quantum computer with a number of quantum bits feasible in the near future (e.g. 40−50). Following the quantum-circuit model of quantum computation, the present works shows the quan...

Most flows of practical interest consist of a mixture of gases. Therefore, the ability to model a gas mixture flow is important. Kinetic models for multicomponent gases have been considered since the original Bhatnagar–Gross–Krook (BGK) model was formulated. BGK-derived models pose a number of difficulties, e.g., avoiding negative density and tempe...

In this work computational fluid dynamics is used to validate experimental results for a two-bladed small rotor In Ground Effect conditions. The paper focuses on the evaluation and prediction of the rotor outwash generated in ground effect. Time-averaged outflow velocities are compared with experimental results, and the simulated flow field is used...

Reynolds Averaged Navier Stokes simulation (RANS) using the in-house CFD solver of Glasgow University is utilized to investigate the flow physics and the sensitivity to modelling assumptions of a multiple shock wave turbulent boundary layer interaction in a rectangular duct (M r = 1.61, Re δr = 162000). Such interactions often occur in high-speed i...

In this work, computational fluid dynamics is used to compare experimental results for a two-bladed small rotor Out of Ground Effect and In Ground Effect conditions. The paper focuses on the evalutation and prediction of the performance of the rotor and investigates the outwash generated in ground effect. Time and phase averaged outflow velocities...

The formulation of computationally efficient methods describing gas mixtures at kinetic level suitable for demanding aerospace applications presents significant challenges. This work presents a gas-kinetic scheme for binary gas mixtures in which the kinetic model is capable of recovering, in the continuum limit, the correct heat transfer, mixture v...

Many high-speed flows of engineering and scientific importance involve gas mixtures. Accounting for the species diffusion in such flows is essential when strong species gradients and temperature gradients occur. The domain of possible applications includes hypersonic rarefied gases, chemical reacting flows and plasmas. Kinetic models for multicompo...

Gas mixtures are important for many practical applications. Extending kinetic model equations of the Bhatnagar–Gross–Krook (BGK) type from a single-species gas to a multi-species gas mixture presents a number of significant challenges. First, obtaining the correct species diffusions, viscous stresses as well as heat conduction in the continuum limi...

The paper presents CFD results for the wake of a helicopter flying a low altitude at different advance ratios. The wakes are assessed in terms of topology and velocity magnitudes. The structure of the wake near ground changes rapidly with the advance ratio and its decay appears to be faster than what is suggested by theoretical analyses. The result...

The paper presents CFD results for the wake of a helicopter flying a low altitude at different advance ratios. The wakes are assessed in terms of topology and velocity magnitudes. The structure of the wake near ground changes rapidly with the advance ratio and its decay appears to be faster than what is suggested by theoretical analyses. The result...

In this work Computational Fluid Dynamics is used as a tool for rotor outwash evaluation. The paper concentrates on the validation of the method, presents different modelling approaches and concludes with suggestions on the use of the method for detailed simulations of rotor outwash. The required computer resources for the detailed computations...

Shock interactions can have a significant impact on heating rates and aerodynamic performance of hypersonic vehicles. The study presents different shock interactions in partially rarefied hypersonic flows predicted employing a recently developed gas-kinetic scheme for diatomic gases with rotational degrees of freedom. The new gas-kinetic schemes wi...

This paper details a real time Lattice Boltzmann solver for computing unsteady wakes. The formulation of the lattice Boltzmann method is first presented followed by a discussion of boundary conditions. This is followed by the details of how the basic algorithm was improved to increase single-core efficiency. A discussion of high Reynolds number imp...

The development and evaluation of quantum computing algorithms for computational fluid dynamics is described. A hybrid classical/quantum hardware approach is assumed where selected computationally intensive parts of the solver are implemented as quantum circuits. The vortex-in-cell method is considered as an example where the Quantum Fourier Transf...

The development of high-performance computing and computational fluid dynamics methods have evolved to the point where it is possible to simulate complete helicopter configurations with good accuracy. Computational fluid dynamics methods have also been applied to problems such as rotor/fuselage and main/tail rotor interactions, performance studies...

Circulation control via blowing over Coanda surfaces at transonic freestream Mach numbers is investigated using numerical simulations. The performance and sensitivity of several circulation control devices applied to a supercritical aerofoil are assessed. Different Coanda devices were studied to assess the effect of Coanda radius-to-slot height rat...

This chapter demonstrates the potential effect of a Gurney flap on the performance of the W3-Sokol rotor blade in hover. A rigid blade was first considered and the calculations were conducted at several thrust settings. The Gurney flap was extended from 46%R to 66%R and it was located at the trailing edge of the main rotor blade. Four different siz...

This chapter presents CFD results for the performance of the W3 Sokol rotor in forward flight and an investigation of the potential effect of the implementation of an active Gurney. Rigid and elastic blade models were considered and calculations were guided using flight test data. The Gurney flap was extended from 40 %R to 65 %R and was located at...

The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the local-correlation–based transition modeling concept represents a valid way t...

This paper begins by comparing turbulence models for the prediction of hybrid air vehicle (HAV) flows. A 6 : 1 prolate spheroid is employed for validation of the computational fluid dynamics (CFD) method. An analysis of turbulent quantities is presented and the Shear Stress Transport (SST) k-ω model is compared against a k-ω Explicit Algebraic Stre...

The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way...

This paper reports on a numerical investigation of the use of trailing-edge circulation control as a roll effector on a generic unmanned combat aerial vehicle: the DLR-F19 stability and control configuration. The Coanda effect induced by fluidic injections at the trailing edge of a wing is used to increase circulation and generate lift. Reynoldsave...

Circulation control simulations were conducted on the SACCON demonstrator UCAV at M = 0.7 with supersonic jets over Coanda surfaces. A comparison is made between a stepped and an unstepped Coanda geometry which showed that the stepped design performed similarly to both simulations and experiments of a like–for–like 10 • flap deflection. Detachment...

This paper presents a study of the W3-Sokol main rotor equipped with Gurney flaps. The effect of the active Gurney is tested at low and high forward flight speeds to draw conclusions about the potential enhancement of the rotorcraft performance for the whole flight envelope. The effect of the flap on the trimming and handling of a full helicopter i...

Waverider will endure the huge aero-heating in the hypersonic flow, thus, it need be blunt for the leading edge. However, the aerodynamic performance will decrease for the blunt waverider because of the drag hoik. How to improve the aerodynamic performance and reduce the drag and aero-heating is very important. The variable blunt radii method will...

Approaches to predict flowfields that display rarefaction effects incur a cost in computational time and memory that is considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flowfields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work, analyticall...

This paper presents an aerodynamic analysis of the flow around a Hybrid Air Vehicle (HAV) in complex flow conditions. The work begins with the validation of the CFD method using a 6:1 prolate spheroid, which showed good agreement with experiments. Subsequently, the Airlander 10 airship of Hybrid Air Vehicles Ltd. was used for the analysis of the role...

Flows around rotor blade sections equipped with active flaps with a degree of freedom in the flap deflection angle are considered in this paper. Results for oscillating flaps are presented. The resultant flap motion was found to couple with the unsteady air loads for cases of blade section in oscillatory translation.

This paper presents the performance analysis and design of a ducted propeller for lighter-than-air vehicles. High- fidelity CFD simulations were undertaken on a model with simplified geometry to quantify the effect of the duct, and to assess the influence of the blade twist on the ducted propeller performance. It is shown that the duct is particularly...

Gradient based optimisation of a Coanda surface for a transonic, supercritical circulation control aerofoil is presented. Design variable updates are driven by a Sequential Least Squares Quadratic Programming (SLSQP) algorithm, using gradients provided by the solution of the Adjoint equations in discrete formulation. Surface sensitivities of the li...

This paper presents an aerodynamic study of bodies related to lighter than air vehicles, using Computational Fluid Dynamics. The work begins with the validation of the CFD method using a 6:1 prolate spheroid. The validated method is then employed for the study of the flow around a shape similar to the Airlander aircraft of Hybrid Air Vehicles Ltd. A...

In this paper, simulation is considered of flow around flapped rotor sections with a degree of freedom in the flap deflection angle. For steady state validation, comparisons one made of numerical results for the flow around a flapped wing with experimental data. Modelling of a blade section with an 1-DOF aeroelastic flap is also considered.

This work explores the breakdown of the wake downstream of the Model Experiments in Controlled Conditions Project (known as the MEXICO project) wind-turbine rotor and assesses the capability of computational fluid dynamics in predicting its correct physical mechanism. The wake is resolved on a fine mesh able to capture the vortices up to eight roto...

Simulations of circulation control via blowing over Coanda surfaces at freestreams up to Mach 0.8 are presented. Validation was conducted against experiments performed at NASA on a 6 percent thick elliptical circulation control aerofoil, which demonstrates the necessary grid requirements and compares between two-equation turbulence models of the k...

This paper presents an aerodynamic and aeroelastic analysis of the MEXICO wind turbine, using the compressible HMB solver of Liverpool. The aeroelasticity of the blade, as well as the effect of a low-Mach scheme were studied for the zero-yaw 15m/s wind case and steady- state computations. The wake developed behind the rotor was also extracted and c...

Operating helicopters in a naval environment is challenging because it imposes a pilot workload significantly higher than that during land-based operations. The aerodynamic interaction between the aircraft and the ship wake is known to play an important role in increasing the pilot workload, hence reducing the aircraft capability as a result of mai...

This paper presents aeroelastic analyses of wind turbines, using the compressible flow Helicopter Multi-Block (HMB2) solver of Liverpool University, coupled with a Computational Structural Dynamics method. For this study, the MEXICO and NREL Phase VI wind turbines were employed. A static aeroelastic method was first employed for the analysis of the...

At the University of Liverpool, the Helicopter Multi-Block (HMB2) CFD code is used for studies of various subsonic and transonic flows. This paper presents the implicit implementation in HMB2 of the AUSM(+) and AUSM(+)up, with a fully analytical Jacobian, so that a wider range of Mach numbers can be modelled, including high-speed flows. A descripti...

This work explores the breakdown of the wake downstream of the MEXICO rotor and assesses the capability of CFD in predicting its correct physical mechanism. The wake is resolved on a fine mesh able to capture the vortices up to 8 radii downstream of the blades. At a wind speed of 15m/s, the main frequency present in the CFD signals for up to 4 radi...

This paper presents a computational investigation of the wake of the MEXICO rotor. The compressible multi-block solver of Liverpool University was employed, using a low-Mach scheme to account for the low-speed flow near the blade and in the wake. In this study, computations at wind speeds of 10, 15 and 24 m s − 1 were performed, and the three compo...

This work explores the breakdown of the wake downstream of the MEXICO rotor and assesses the capability of CFD in predicting its correct physical mechanism. The wake is resolved on a fine mesh able to capture the vortices up to 8 radii downstream of the blades. At a wind speed of 15m/s, the main frequency present in the CFD signals for up to 4 radi...

This paper presents CFD results for the performance of the W3-Sokol rotor in forward flight and the potential effect of the implementation of an active Gurney flap. A rigid blade was considered and calculations were conducted based on flight test data. The Gurney flap was extended from 40%R to 65%R and it was located at the trailing edge of the bla...

Interactional effects between the main rotor and the fuselage of a helicopter are important for the performance analysis of helicopters especially near the edges of the helicopter flying envelope. Computational Fluid Dynamics is also capable of quantifying these effects although a substantial computational cost. At the same time, assessment and val...

The development of High Performance Computing and CFD methods have evolved to the point where it is possible to simulate complete helicopter configurations with a good accuracy. These capabilities have been applied to a variety of problems such as rotor/fuselage and main-tail rotors interactions, helicopter performance in hover and forward flight,...

This paper presents the implementation of all‐Mach Roe‐type schemes in a fully implicit CFD solver. Simple 2D cases, such as the flow around inviscid and viscous aerofoils, were used for an initial validation of these methods, along with more challenging computations consisting of the 3D flow around the Model Experiments in Controlled Conditions wi...

This paper focuses on coupling methods for hybrid Navier–Stokes/molecular dynamics (MD) simulations. The computational domain is split in a continuum flow region, where a finite-volume discretisation of the Navier–Stokes equations is used, and one or more particle domains, where molecular level modelling of the flow is employed. The domains are def...

High Performance Computing (HPC) is necessary in the analysis of complex flows using Computational Fluid Dynamics (CFD) since it allows problems to be tackled within realistic time scales or it allows for new problems to be explored. In recent years, the exponential growth of computing performance was also combined with the increasing availability...

The GOAHEAD project, funded under the 6th European Funding framework, provided valuable measurements of flow parameters for a realistic helicopter configuration. The wind tunnel investigations included an extensive set of conditions from cruise at high speed, to very high speed flight as well as high disk loading cases. Several GOAHEAD partners, in...

A novel experimental and computational aerodynamic database for a complete helicopter has been generated for the GOAHEAD project. The primary objective of the five-year long project was to validate state-of-the-art CFD solvers developed for rotorcraft aerodynamic problems against experimental measurements. The present work is focused on the CFD asp...

The present work focuses on coupling discrete-velocity methods for the kinetic Boltzmann (BGK, BGK-Shakhov) equations with finite-volume methods for the compressible-flow Navier-Stokes equations. This is achieved within a computational framework for multi-physics simulations, built on the concept of generic programming and object-orientation. The p...

This paper presents a comparative study of several Detached-Eddy Simulation closures for a ship air wake. The experiments of the National Research Council of Canada for the Simple Frigate Shape 2 are used to validate the employed Computational Fluid Dynamics method at two wind angles. The CFD results show that URANS and DES are capable of predictin...

A method able to model the aerodynamics and aeroelastics of flapped rotors is presented in this paper. The structural model of the blade and the associated mesh deformation algorithms are tested for several cases with good results. In addition, a 1-DOP model is introduced for the flaps and several techniques are put forward for the coupled CFD/CSD...

In this paper, we contribute a multi-scale method based on an iterative operator splitting method, which takes into account the dis-parity of the macro-and microscopic scales. We couple Navier Stokes and Molecular Dynamics equations, while taken into account their un-derlying scales. Combining relaxation methods and averaging techniques we can opti...

As rotorcraft requirements for higher performance, low vibration and low noise become stricter, CFD methods become a necessary tool for the analysis of new rotor designs. In parallel, the widespread interest in flapped rotors sets new challenges for CFD. In this paper, a demonstration of the Helicopter Multi-Block CFD solver for the analysis of sma...

Detached-Eddy Simulations (DES) of flows over clean and controlled cavities with and without doors are presented in this paper. Mach and Reynolds numbers (based on cavity length) were 0.85 and one million respectively. Spectral analyses showed that the DES computations were able to correctly predict the frequencies of the Rossiter modes for both un...