Waqar Asrar

Implicit Gas-Kinetic Bhatnagar-Gross-Krook Scheme for Compressible Flows

A gas-kinetic scheme based on the Bhatnagar‐Gross‐Krook (BGK) model is developed for two-dimensional compressible inviscid flowfields. The BGK scheme is an approximate Riemann solver that uses the collisional Boltzmann equation as the governing equation for flow evolutions. For efficient computations, particle distribution functions in the general solution of the BGK model are simplified and used for the flow simulations. High-order accuracy is achieved via the reconstruction of flow variables using the MUSCL interpolation technique. For steadystate problems, the approximate factorization‐alternating direction implicit implicit time integration method is adopted, which is preferable to a multistage Runge‐Kutta method. To investigate the computational characteristics of BGK scheme in detail, it has been applied to various two-dimensional numerical experiments. The results, compared with some typical schemes, such as the Steger‐Warming flux vector splitting and Roe flux difference splitting, as well as exact solutions, are found to be robust and accurate, and to have high resolution at discontinuities such as shock waves.

Development of Gas-Kinetic BGK Scheme for Two- Dimensional Compressible Inviscid Flows

In this paper, a gas-kinetic scheme based on the BGK (Bhatnagar-Gross-Krook) model is developed for the two-dimensional compressible inviscid flow fields. BGK scheme is an approximate Riemann solver that uses the collisional Boltzmann equation as the governing equation for flow evolutions. For efficient computations, particle distribution functions in the general solution of the BGK model are simplified and used for the flow simulations. High order accuracy is achieved via the reconstruction of flow variables using the MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) interpolation technique. For steady state problems, an implicit time integration method is adopted here which is more preferable to a multi-stage Runge-Kutta method. To investigate the computational characteristics of BGK scheme in detail, it has been applied to two typical two-dimensional numerical experiments namely, a supersonic wedge and a channel with ramp. The results, compared with some typical schemes like those Steger-Warming (SW) FVS (Flux Vector Splitting), and Roe FDS (Flux Difference Splitting) and available exact solutions are summarized as follows; robust, accurate and high resolution at discontinuities such as shock waves.

Investigation of Aerodynamic Parameters of a Hybrid Airship

The aerodynamic parameters of a preliminary winged-hull airship design are investigated. The research methodology involved the use of numerical simulation and wind tunnel testing. The aerodynamic parameters of the design are first computed using a commercial CFD code. The force and moment coefficients are then measured on a scaled model in the IIUM low speed wind tunnel. The experimental results generally agree with the CFD predicted data. Addition of a wing to conventional airship increases the lift substantially with a reasonable increase in drag. The longitudinal and directional stabilities were found to be statically stable, however, both the conventional airship and the hybrid airship were found to have poor rolling stability. CFD simulations show that modifications to the wing placement and its dihedral have strong positive effect on the rolling stability.

Study of the Reverse Delta Wing

Particle image velocimetry was used in a low-speed wind tunnel to investigate the vortex structures of a slender reverse delta wing at various angles of attack and roll. This work investigates the characteristics of the vortices generated downstream in planes perpendicular to the freestream direction and their dependence on angles of attack and roll at a chord-based Reynolds number of Rec= 382000 The peak tangential velocities at�angle of attack higher than 5 deg show a trend similar to a delta wing. A six-component balance was used to obtain the aerodynamic coefficients for a reverse delta wing as well as a delta wing for comparison. A simulation of the streamlines, velocity vectors, and surface pressure contours was carried out using computational fluid dynamics software to show the characteristics of the flow over a reverse delta wing.

Conceptual design of a winged hybrid airship

The present study focuses on the sizing and aerodynamic contour design of a two-seater 1000 kg gross take-off mass winged hybrid airship. Unlike the conventional hybrid airships, which stay aloft and takeoff with the help of VTOL propulsion systems, a winged hybrid airship requires a certain speed to takeoff by utilizing lift coming from its aerodynamic surfaces. Heaviness fraction and takeoff ground roll are considered as measure of merit in initial sizing. Based on the design requirement of Malaysian inter-island tourism and transportation of agricultural products, range is set to 450 km and ground roll for take-off about 150 m. For the airship to be heavy enough for ground handling, the ratio of hydrostatic to hydrodynamic lift is set equal to 49:51. Summary of the results to be obtained in early design phase will give a baseline start to study the aerodynamics and stability characteristics of such airships in future.

EVALUATION OF GAS-KINETIC SCHEMES FOR SOLVING 1D INVISCID COMPRESSIBLE FLOW PROBLEMS

In this paper, two classes of gas-kinetic schemes are investigated for one-dimensional compressible inviscid flow, namely, the Kinetic Flux Vector Splitting (KFVS) scheme and the Bhatnagar-Gross-Krook (BGK) scheme. Second-order high-resolution scheme for both methods are also developed for calculating flows containing discontinuities. This is achieved by means of reconstructing the initial data via Monotone Upstream-Centered Schemes for Conservation Laws (MUSCL) approach. The Total Variation Diminishing (TVD) shock capturing properties of these second-order schemes are achieved through the use of non-linear limiters. In addition, a multistage TVD Runge-Kutta method is employed for the time integration of the finite volume gas-kinetic scheme. Exclusive consideration is focused on the BGK scheme, which yields a better numerical result in comparison with the KFVS scheme. Three typical one-dimensional inviscid flow problems containing shocks, namely, steady flow in a divergent nozzle, the unsteady shock tube problem, and two interacting blast waves problem are analyzed numerically with the gas-kinetic schemes. Numerical results from the first-order and second-order gas-kinetic schemes are presented and compared with the exact solutions. Other computed results such as those from the Steger-Warmings Flux Vector Splitting scheme, Roes Flux Difference Splitting scheme, MacCormacks scheme, and high-order compact Van Leers Flux Splitting Scheme are also presented as comparisons to the gas-kinetic schemes. In addition, the effects of grid sizes on the numerical results of the gas-kinetic schemes are also investigated.

Higher Order Compact-Flowfield Dependent Variation (HOC-FDV) Solution of One-Dimensional Problems

Abstract In this paper, a novel higher order accurate scheme, namely high order compact flowfield dependent variation (HOC-FDV) method has been used to solve one-dimensional problems. The method is fourth order accurate in space and third order accurate in time. Four numerical problems; the nonlinear viscous Burger’s equation, transient Couette flow, the shock tube (Sod problem) and the interaction of two blast waves are solved to test the accuracy and the ability of the scheme to capture shock waves and contact discontinuities. The solution procedure consists of tri-diagonal matrix operations and produces an efficient solver. The results are compared with analytical solutions, the original FDV method, and other standard second order methods. The results also show that HOC-FDV scheme provides more accurate results and gives excellent shock capturing capabilities.

Application of Gas-Kinetic BGK Scheme for Solving 2-D Compressible Inviscid Flow around Linear Turbine Cascade

Fluid flows within turbomachinery tend to be extremely complex. Understanding such flows is crucial in the effort to improve current turbomachinery designs. Hence, computational approaches can be used to great advantage in this regard. In this paper, gas-kinetic BGK (Bhatnagar-Gross-Krook) scheme is developed for simulating compressible inviscid flow around a linear turbine cascade. BGK scheme is an approximate Riemann solver that uses the collisional Boltzmann equation as the governing equation for flow evolutions. For efficient computations, particle distribution functions in the general solution of the BGK model are simplified and used for the flow simulations. Second-order accuracy is achieved via the reconstruction of flow variables using the MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) interpolation technique together with a multistage Runge-Kutta method. A multi-zone H-type mesh for the linear turbine cascades is generated using a structured algebraic grid generation method. Computed results are compared with available experimental data and found to be in agreement with each other. In order to further substantiate the performance of the BGK scheme, another test case, namely a wedge cascade, is used. The numerical solutions obtained via this test are validated against analytical solutions, which showed to be in good agreement.

Gas-Kinetic BGK Scheme for Hypersonic Flow Simulation

In this paper, the BGK (Bhatnagar-Gross-Krook) scheme is extended to hypersonic flow simulations and thus shows that the compressible inviscid flow solutions of the simulations are efficiently and accurately obtained from the BGK scheme without the disastrous shock instability phenomenon that occurs in most hypersonic flow simulations involving strong shock waves. For this particular study, the effect of chemistry in hypersonic flows has not been taken into account. Hence, the assumption of calorically perfect gas is imposed in all simulations. The high-order resolution of the scheme is achieved by utilizing MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws)-type initial reconstruction. While, an implicit-type time integration method known as the AF-ADI (Approximate Factorization - Alternating Direction Implicit) is adopted for computing both steady and unsteady computations. Two typical hypersonic flow problems are selected in this study in order to test the gas-kinetic schemes characteristics and performance, namely, the blunt body, and the double Mach reflection problems. The numerical findings of the BGK scheme via these tests indicate that this technique is robust, accurate and stable for hypersonic flow.

Induced rolling moment for NACA4412 plain and flapped wing

Purpose – The paper aims to compute rolling moments on a follower aircraft wing due to vortices generated by a plain and flapped NACA4412 wing using experimental particle image velocimetery (PIV) data.Design/methodology/approach – This paper describes the detailed variation of the induced rolling moment on a follower aircraft wing derived from a PIV velocity field measurement. A rectangular wing of a subsonic wall interference model is used as a vortex generator in two different configurations: plain wing of NACA4412 cross‐section profile; and flapped wing with trailing edge flap of NACA0012 cross‐section profile extended at 20°.Findings – Results obtained showed that the maximum induced rolling moment coefficient depends on the strength of the vortex produced by the generating aircraft wing and increases linearly with the increment of the angle of attack.Originality/value – This paper provides an insight on the effects of different angles of attacks for plain and flapped wings on the induced rolling mome...