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The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems, using parallel algorithm.

Parallel solution to the 3‐D incompressible full Navier‐Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time‐step sizes, with Courant‐Friedrichs‐Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non‐overlapping sub‐domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3‐D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied.

It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely.

A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well‐known 3D free‐convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re=2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re=2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.

Oil-free heat pumps that use the system refrigerant gases as lubricants are preferred for thermal management in future space applications. This study aims to numerically and experimentally investigate the static performance of externally pressurized thrust bearings lubricated with refrigerant gases.

The refrigerant gases R22, R410A and CO₂ were chosen as the research objects, while N₂ was used for comparison. Computational fluid dynamics was used to solve the full 3 D Navier–Stokes equations to determine the load capacity, static stiffness and static pressure distribution in the bearing film. The numerical results were experimentally verified.

The results showed that the refrigerant-gas-lubricated thrust bearings had a lower load capacity than the N2-lubricated bearings, but they presented a higher static stiffness when the bearing clearance was less than 9 µm. Compared with the N2-lubricated bearings, the optimal static stiffness of the R22- and CO2-lubricated bearings increased by more than 46% and more than 21%, respectively. The numerical and experimental results indicate that a small bearing clearance would be preferable when designing externally pressurized gas thrust bearings lubricated with the working medium of heat pump systems for space applications.

The findings of this study can serve as a basis for the further investigation of refrigerant gases as lubricants in heat pump systems, as well as for the future design of such gas bearings in heat pump systems for space applications.

The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows characterized by multiple speeds, multiple physical phenomena, and by large variations in flow variables.

Fundamentally, the FDV method may be regarded as a variant of the Lax-Wendroff Scheme (LWS) that is obtained by replacing the explicit time derivatives in LWS by a weighted combination of explicit and implicit time derivatives. The weighting factors – referred to as FDV parameters – may be broadly classified as convective and diffusive parameters which, for example, are determined using flow quantities such as the Mach number and Reynolds number, respectively. Hence, the reference to these parameters and the method as “flow field dependent.” A von Neumann Fourier analysis demonstrates that the increased implicitness makes FDV both more stable and less dispersive compared to LWS, a feature crucial to capturing shocks and other phenomena characterized by high gradients in variables. In the current study, the FDV scheme is implemented in a Taylor-Galerkin-based finite element method framework that supports arbitrarily high order, unstructured isoparametric elements in one-, two- and three-dimensional geometries.

At first, the spatial accuracy of the implemented FDV scheme is established using the Method of Manufactured Solutions, wherein the results show that the order of accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one. The dispersion and dissipation errors of FDV, when applied to the compressible Navier-Stokes and energy equations, are investigated using a 2-D, small-amplitude acoustic pulse propagating in a quiescent medium. It is shown that FDV with third-order shape functions accurately captures both the amplitude and phase of the acoustic pulse. The method is then applied to cases ranging from low-Mach number subsonic flows (Mach number M=0.05) to high-Mach number supersonic flows (M=4) with shock-boundary layer interactions. For all cases, fair to good agreement is observed between the current results and those in the literature.

The spatial order of accuracy of the FDV method, its stability and dispersive properties, as well as its applicability to low- and high-Mach number flows are established.

This paper seeks to increase our understanding on the fluid mechanics and heat transfer in a transitional mixed convection flow between two vertical plates. Direct numerical simulation by the spectral method, with a weak formulation, is used to solve the transient 3–D Navier‐Stokes equations and energy equation. Initial disturbances consist of the finite‐amplitude 2–D Tollmien‐Schlichting wave and two 3–D oblique waves. The transition phenomena in a mixed‐convection flow can be significantly different from the isothermal flow. Disturbance competitions among different modes are also found to be different from those known for an isothermal flow. In a mixed‐convection flow, there exist thresholds for the low‐mode Fourier waves. The intensified vortices are concentrated left of the central surface between the two plates. Hairpin vortices are formed with high Ri. Based on the flow visualization, the λ vortices are found to be staggered on the surfaces parallel to the plates. The Ri number seems to be the main parameter governing the transition mechanism. The Nu number is found to increase during transition.

The suitability of a coupled scheme based on parabolic/elliptic Navier‐Stokes equations for calculating film cooling flows and heat transfer downstream of flush, angled injection slots is explored. The coupled algorithm that combined the coarse mesh ‘outer’ Navier‐Stokes and fine grid ‘inner’ parabolic Navier‐Stokes codes makes retention of the current high resolution model desirable because an acceptable accuracy and economy of computation time are attainable using only mini‐computer resources. The ‘inner‐code’ includes the FLARE approximation to permit small reverse flow. The inner and outer codes are coupled by adopting an approach analogous to classical multigrid methods. It is found that for high blowing mass flow rate of 1.0 with the case of greater than 40° injection angle, the fully parabolic procedure is unable to cope with an extensive separation region immediately downstream of the slot; the present coupling methodology is crucial. The study involves the calculation of heat transfer rates on the surface downstream of the angled slot. Predicted film cooling effectiveness distribution together with the effects of governing parameters are described and show close agreement with the experimental data.

This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows.

The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure.

A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy.

This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

PHOENICS, a general 3‐D Navier‐Stokes computer program, was used to simulate cooling and freezing of jet fuel stored in airplane fuel tanks. A 3‐D analysis is required for fuel tanks of arbitrary geometry exposed to time dependent and nonuniform boundary temperatures. The work reported in this paper concentrated on 2‐D simulations of fuel cooling and freezing in a wing tank and external (pylon) tanks as a step toward the 3‐D analysis. Significant progress has been made on obtaining plausible solutions over the entire range of conditions considered. The same model, with appropriate changes for fuel properties, could also be used to predict fuel heating in airplane fuel tanks during supersonic flight conditions.

The averaged Navier‐Stokes and the k‐e turbulence model equations are used to simulate turbulent flows in some internal flow cases. The discrete equations are solved by different variations of Multigrid methods. These include both steady state as well as time dependent solvers. Locally refined grids can be added dynamically in all cases. The Multigrid schemes result in fast convergence rates, whereas local grid refinements allow improved accuracy with rational increase in problem size. The applications of the solver to a 3‐D (cold) furnace model and to the simulation of the flow in a wind tunnel past an object prove the efficiency of the Multigrid scheme with local grid refinement.

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows around rotational parts of aircraft.

The computational domain is decomposed into two sub-domains, namely, the rotational sub-domain which contains the rotational boundaries, and the stationary sub-domain which contains the remainder flow field including the stationary boundaries. The artificial boundaries and restriction boundaries are used as the restriction condition to generate the entire computational grid, and then the overset grids are established according to the radius parameters of artificial boundaries set previously. The deformation of rotational boundary is treated by using the linear spring analogy method which is suitable for the dynamic unstructured grid. The unsteady Navier-Stokes/Euler equations are solved separately in the rotational sub-domain and stationary sub-domain, and data coupling is accomplished through the overlapping area. The least squares method is used to interpolate the flow variables for the artificial boundary points with a higher calculating precision. Implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) time stepping scheme is implemented to accelerate the inner iteration during the unsteady simulation.

The airfoil steady flow, airfoil pitching unsteady flow, three-dimensional (3-D) rotor flow field, rotor-fuselage interaction unsteady flow field and the flutter exciting system unsteady flow field are numerically simulated, and the results have good agreements with the experimental data. It is shown that the present method is valid and efficient for the prediction of complicated unsteady problems which contain rotational dynamic boundaries.

The results are entirely based on computational fluid dynamics (CFD), and the 3D simulations are based on the Euler equations in which the viscous effect is ignored. The current work shows further applicable potential to simulate unsteady flow around rotational parts of aircraft.

The current study can be used to simulate the two-dimensional airfoil pitching, 3-D rotor flow field, rotor-fuselage interaction and the flutter exciting system unsteady flow. The work will help the aircraft designer to get the unsteady flow character around rotational parts of aircraft.

A new type of rotational dynamic overset grids is presented and validated, and the current work has a significant contribution to the development of unstructured rotational dynamic overset grids.

The purpose of this paper is to present an engineering inviscid‐boundary layer method for the calculation of convective heating rates on three‐dimensional non‐axisymmetric geometries at angle of attack.

Based on the axisymmetric analog, convective heating rates are calculated along the surface streamlines which are determined using the inviscid properties calculated on an unstructured grid.

Since the method is capable of using inviscid properties calculated on an unstructured grid, it is applicable to a variety of configurations and it requires much less computational effort than a Navier‐Stokes code. The results of the present method are evaluated on different wing body configurations in laminar and turbulent hypersonic equilibrium flows. In comparison to experimental data, the present results are found to be fairly accurate in the windward and leeward regions.

With this approach, heating rates can be predicted on general three‐dimensional configurations at hypersonic speeds in an accurate and fast scheme.

In order to calculate the heating rates at any specific point on the surface, a technique is developed to calculate the inviscid surface streamlines in a backward manner using the inviscid velocity components. The metric coefficients are also calculated using a new simple technique.