Thin-layer Navier-Stokes Research Articles

Dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric transitional/turbulent flows

An appropriate combination of the thin-layer Navier–Stokes (TLNS) and parabolized Navier–Stokes (PNS) solvers is used to accurately and efficiently compute hypersonic transitional/turbulent flowfields of perfect gas and equilibrium air around blunt-body configurations. The TLNS equations are solved in the nose region to provide the initial data plane needed for the solution of the PNS equations. Then the PNS equations are employed to efficiently compute the flowfield for the afterbody region by using a space marching technique. Both the TLNS and the PNS equations are numerically solved by using the implicit non-iterative finite-difference algorithm of Beam and Warming. A shock fitting procedure is used in both the TLNS and PNS codes to obtain accurate solution in the vicinity of the shock. For turbulent flow simulations, both the Cebeci–Smith (CS) and the Baldwin–Lomax (BL) turbulence models are analyzed with the present technique for the case of long slender blunt bodies. The Baldwin–Lomax turbulence model, which does not need the determination of the edge of the boundary layer, is modified in the present work to include the effects of variable properties and damping factor to accurately calculate flowfield characteristics in turbulent regions. Detailed comparisons are made with other numerical and experimental results to assess the accuracy and efficiency of the present solution procedure for computing hypersonic transitional/turbulent flows over long slender blunt bodies. The results of these computations are found to be in good agreement with available data. The effects of real gas on the flowfield characteristics are also studied.

Computational and Experimental Investigations of Boundary Layer Tripping

Supersonic flow over a tapered body of revolution has been investigated both experimentally and numerically. The experimental study consisted of a series of wind tunnel tests on an ogive-cylinder body. Static pressure distributions on the body surfaces at several longitudinal cross sections, as well as the boundary layer profiles at various angles of attack have been measured. Further, the flow around the model was visualized using Schlieren technique. Tests with a natural development of the boundary layer and with tripping were also carried out. All tests were conducted in the trisonic wind tunnel of Qadr Research Center. Our results show that artificial boundary layer tripping has minor effect on the static surface pressure distribution (depending on its diameter and installation location), while the changes in total pressure around the body were significant. Tripping the boundary layer increased its thickness, changed its profile particularly near the body surface. Two oblique shock waves were formed in the front and behind the trip wire. In this study, using multi-block grid, the thin layer Navier-Stokes (TLNS) equations were solved around the above models. Also patched method was used near the interfaces. Good agreements were achieved when the numerical results were compared with the corresponding experimental data.

Dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric laminar flows

An appropriate combination of the thin-layer Navier–Stokes (TLNS) and parabolized Navier–Stokes (PNS) solvers is used to accurately and efficiently compute hypersonic flowfields of equilibrium air around blunt-body configurations. The TLNS equations are solved in the nose region to provide the initial data plane needed for the solution of the PNS equations. Then the PNS equations are employed to efficiently compute the flowfield for the afterbody region by using a space marching procedure. Both the TLNS and PNS equations are numerically solved by using the efficient implicit non-iterative finite-difference algorithm of Beam and Warming. A shock fitting technique is used in both the TLNS and PNS codes to obtain accurate solution in the vicinity of the shock. In the regions of the flowfield with upstream influences, the globally iterated PNS (IPNS) equations, which are computationally more efficient than the TLNS equations, can be used to improve the accuracy of the results. To validate the results of the developed TLNS code and study real gas effects on the flowfield, hypersonic laminar flow over a sphere at Mach number of 11.26 is computed. The computations are performed for hypersonic laminar flow over 5° long slender blunt cone at Mach number of 19.25 to demonstrate the accuracy and efficiency of using the present TLNS-PNS methodology. To show the capability and robustness of the present solution procedure, the comparisons are also made with the wall heat-transfer data on a 12.84 ° / 7 ° bicone at Mach number of 6.89 and freestream temperature of 1604 K. The results of these computations are found to be in good agreement with available numerical and experimental data. The results of the perfect gas for these cases are also presented and the effects of real gas on the flowfield characteristics are studied in both the TLNS and PNS solutions.

On the Use of High-Order Accurate Solutions of PNS Schemes as Basic Flows for Stability Analysis of Hypersonic Axisymmetric Flows

Abstract High-order accurate solutions of parabolized Navier–Stokes (PNS) schemes are used as basic flow models for stability analysis of hypersonic axisymmetric flows over blunt and sharp cones at Mach 8. Both the PNS and the globally iterated PNS (IPNS) schemes are utilized. The IPNS scheme can provide the basic flow field and stability results comparable with those of the thin-layer Navier–Stokes (TLNS) scheme. As a result, using the fourth-order compact IPNS scheme, a high-order accurate basic flow model suitable for stability analysis and transition prediction can be efficiently provided. The numerical solution of the PNS equations is based on an implicit algorithm with a shock fitting procedure in which the basic flow variables and their first and second derivatives required for the stability calculations are automatically obtained with the fourth-order accuracy. In addition, consistent with the solution of the basic flow, a fourth-order compact finite-difference scheme, which does not need higher derivatives of the basic flow, is efficiently implemented to solve the parallel-flow linear stability equations in intrinsic orthogonal coordinates. A sensitivity analysis is also conducted to evaluate the effects of numerical dissipation and grid size and also accuracy of computing the basic flow derivatives on the stability results. The present results demonstrate the efficiency and accuracy of using high-order compact solutions of the PNS schemes as basic flow models for stability and transition prediction in hypersonic flows. Moreover, indications are that high-order compact methods used for basic-flow computations are sensitive to the grid size and especially the numerical dissipation terms, and therefore, more careful attention must be kept to obtain an accurate solution of the stability and transition results.

Numerical simulation of stage separation manoeuvre with jet interaction

PurposeThis research aims to investigate numerically the influence of braking jets on separation process of a flying object.Design/methodology/approachThe flying object is at supersonic regime and axial separation of its stages is accomplished with the aid of braking jets of separated stage. The simulation is three‐dimensional and relative motion of the stages is considered three degree of freedom. Full Navier‐Stokes equations in conjunction with κ−ε (RNG) turbulence model equations are considered as governing equations. These equations are solved using the finite volume technique. The separation process is analysed as an unsteady process and the problem is solved in a moving grid domain. The local remeshing method is adapted to regenerate computational cells around moving boundaries.FindingsTime history of flow field around the vehicle components, time history of aerodynamic coefficients, and instantaneous relative position of the body components are the results of this research. Numerical modelling results are compared with the results of other references.Originality/valueMost of the similar works in this area have used Euler or thin layer Navier‐Stokes (TLNS) equations as governing equations and the use of full Navier‐Stokes equations to analyse such a complicated problem (3D axial separation with braking jets) have not been reported in the literature. Since there are some recirculation zones inside the flow field and Euler or even TLNS equations cannot predict their behaviours, the use of full Navier‐Stokes equations may lead to more accurate prediction of these regions and aerodynamic forces.

Projectile Performance, Stability, and Free-Flight Motion Prediction Using Computational Fluid Dynamics

With the recent development of capabilities for predicting damping derivatives, it is now possible to predict the stability characteristics and free-flight motion for projectiles using data that are derived solely from computational fluid dynamics (CFD). As a demonstration of the capability, results are presented for a family of axisymmetric projectiles in supersonic flight. The particular configuration selected has been extensively tested in aeroballistic ranges, and high-quality experimental data have been obtained. Thin-layer Navier-Stokes techniques have been applied to compute the attached viscous flow over the forebody of the projectile and the separated flow in the projectile base region. Parameters that characterize the in-flight motion are subsequently evaluated using the predicted aerodynamic coefficients, including the gyroscopic and dynamic stability factors and the projectile's fast- and slow-mode frequencies and damping coefficients. These parameters are then used to predict the free-flight motion of the projectile. In each case, the computational approach is validated by comparison with experimental data, and very good agreement between computation and experiment is found. It is believed that this demonstration represents the first known instance of a viscous CFD approach being applied to predict all of the necessary data for performance of linear aerodynamics stability and trajectory analyses.

Aileron Buzz Simulation Using an Implicit Multiblock Aeroelastic Solver

A fully implicit multiblock aeroelastic solver, which coupled thin-layer Navier-Stokes equations with structural equations of motion, has been developed for the flutter simulation on complex aerodynamic configurations. Navier-Stokes equations are solved with a lower-upper symmetric Gauss-Seidel subiteration algorithm and a modified Harten-Lax-van Leer-Einfeldt-Wada scheme. Structural equations of motion are discretized by a direct second-order differential method with subiteration in generalized coordinates. The transfinite interpolation is used for the grid deformation of the blocks neighboring the flexible surface. To evaluate the effectiveness of the grid deformation, a comparison is first done for the oscillating LANN wing with a rigidly attached grid and a deforming grid. Then the method is applied to predict the flutter speed and frequency of the AGARD 445.6 standard aeroelastic wing. Finally, the aeroelastic instability referred to as aileron buzz is simulated for the supersonic transport model of the National Aerospace Laboratory of Japan.

Accuracy of Parabolized Navier-Stokes Schemes for Stability Analysis of Hypersonic Axisymmetric Flows

The accuracy of the parabolized Navier ‐Stokes (PNS) and globally iterated PNS (IPNS) schemes for use as basic e ows is studied for stability analysis of hypersonic axisymmetric e ow over blunt and sharp slender cones at Mach 8. The numerical solution of the PNS and IPNS models is obtained by using the implicit e nite difference algorithm of Beam and Warming with a shock-e tting procedure. Both the PNS and IPNS solutions are thoroughly verie ed and compared with the thin-layer Navier ‐Stokes (TLNS) solution and experimental data. The stability analysis and transition prediction are performed using theparallel-e owlinearstability theory together with the eN method.Asystematicsensitivitystudyisperformedforbasicstatesolutions,includingproe lesandtheirderivatives, and spatial growth rates obtained from the PNS and IPNS models. The basic e ow and stability results and the predicted transition location based on the PNS model are qualitatively in good agreement with those of other theoretical investigations using various basic e ow models. Improved agreement with the TLNS model for both basic state solution and stability results is achieved when the IPNS model is applied. Attention is concentrated on those features of the numerical methods of the basic e ow computation that need particular care if adequate stability results are to be obtained. The study shows that the number of grid points, the grid distribution, and the amount of numerical dissipation have signie cant effects on the stability results. Moreover, indications are that carefulnumericalsolutionsofthePNSandIPNSschemesaslaminarbasice owcalculationsleadto amorepractical transition prediction tool in hypersonic e ows.

Numerical Analysis of Dynamic Stability of a Reentry Capsule at Transonic Speeds

Dynamic stability of a reentry capsule in transonic speeds is discussed. An unsteady flowfield around the capsule under the forced pitching oscillation in the transonic flow of M = 1.3 is numerically simulated based on the three-dimensional thin-layer Navier-Stokes equations. The numerical result reveals that the dynamic instability is caused by the phase delay of the base pressure. It is also found that the base pressure, the recompression shock wave, and the wake behind the recompression shock wave all oscillate with the same delay time. The flow mechanism is proposed based on the idea that the phase delay of the base pressure is caused by a feedback loop of the flowfield behind the capsule. This flow mechanism reasonably explains the features observed in the present numerical simulation, as well as the experimental fact that the dynamic instability occurs at very low reduced frequencies.

Numerical calibration of a conical five-hole probe for supersonicmeasurements

A miniature conical five-hole probe of 30° half-angle wasnumerically calibrated for measurements of flow properties at supersonic Machnumbers in order to circumvent the traditional experimental approach, vastlydemanding on resources. The principle of a multi-hole conical probe is basedon the notion that Mach number, pressure and directionality of the incomingstream may be correlated with the combination of pressure readings on theconical probe surface and a Pitot port situated at the flat tip. Using athree-dimensional thin layer Navier-Stokes solver, calibration data weregenerated for the range of Mach numbers and pitch angles of interest. Thevalidity of the computed pressure distributions on the probe surface wassubsequently confirmed in a series of wind tunnel tests including low Machnumber and high angularity flow-field. The current study also demonstrated theprofound influence of the blunt tip on the nearby static pressure ports, itsrelevance to the ultimate modelling strategy and the resulting calibrationcharts.

Design optimization of axial flow compressor blades with three-dimensional Navier-Stokes solver

Numerical optimization techniques combined with a three-dimensional thin-layer NavierStokes solver are presented to find an optimum shape of a stator blade in an axial compressor through calculations of single stage rotor-stator flow, Governing differential equations are discretized using an explicit finite difference method and solved by a multi-stage Runge-Kutta scheme. Baldwin-Lomax model is chosen to describe turbulence. A spatially-varying time-step and an implicit residual smoothing are used to accelerate convergence. A steady mixing approach is used to pass information between stator and rotor blades. For numerical optimization, searching direction is found by the steepest decent and conjugate direction methods, and the golden section method is used to determine optimum moving distance along the searching direction. The object of present optimization is to maximize efficiency. An optimum stacking line is found to design a custom-tailored 3-dimensional blade for maximum efficiency with the other parameters fixed.

Multidisciplinary optimization for gas turbine airfoil design

A multidisciplinary optimization procedure for gas turbine airfoil design has been developed and demonstrated on a generic blade. Aerodynamic and heat transfer design objectives are integrated along with various constraints on the airfoil geometry. Heat transfer optimization and external aerodynamic shape optimization has been performed on a generic blade. Shape optimization is performed using geometric parameters associated with film cooling and blade external shape. The blade is cooled both internally and externally (film cooling). Thin layer Navier-Stokes equations are used for the external flow field evaluations and finite element analysis is used to determine the blade interior temperatures. Total pressure loss, exit kinetic energy loss, average blade temperature and maximum blade temperature are minimized, with constraints on the blade geometry. The constrained multiobjective optimization problem is solved using the Kreisselmeier-Steinhauser (K-S) function approach. The results for the generic blade demonstrate the effectiveness of the optimization procedure.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Viscous simulation of F-16 like configuration at high AoA

A viscous simulation of the flow over an F-16A model with inlet and the ventral fins, which were normally not considered in previous studies, is described. The method uses a patch grid multi-block, multi-grid Navier-Stokes solver. A novel method to grid the intake and diverter is used. The arrangement of the gridding system adopted minimises the number of grids needed particularly for viscous computations. A modified form of the Baldwin-Lomax algebraic turbulence model was used for the high AoA studies. To simplify the incorporation of turbulence model, the blocking arrangement is such that it allows a thin-layer Navier-Stokes equation formulation in the calculation of the eddy viscosity. A series of four flow conditions were studied; M = 0.9, AoA = 4°, 6.0°; and M = 1.2 at AoA = 6.0°; and M = 1.85 at AoA = 16°. Extensive comparisons with experimental data of the pressure distribution on the wing and on different streamwise stations show the modelling to be reasonably accurate. For the results presented here, the wing tip missile is ignored.

Unsteady flow around helicopter rotor blade sections in forward flight

AbstractThe aerodynamic performance of aerofoils performing unsteady motions is important for the design of helicopter rotors. In this respect the study of aerofoils undergoing in-plane oscillations (translation along the horizontal axis) provides useful insight into the flow physics associated with the advancing blade in forward flight. In this paper a numerical method is developed in which the unsteady thin layer Navier-Stokes equations are solved for aerofoils performing rigid body motions. The method has been applied to the calculation of the flowfield around a NACA 0012 aerofoil performing in-plane motions representative of high-speed forward flight. Comparison of computed pressure data with experimental measurements is generally found to be good. The quantitative differences observed between computations and experiment are thought to have arisen mainly as a consequence of the low aspect ratio of the model rotor employed in the windtunnel tests.

Shock oscillations on biconvex aerofoils

The mechanism of the origin of shock oscillations on an 18% thick biconvex aerofoil is investigated using a thin-layer Navier-Stokes code. The approach used in this study is to initiate shock oscillations on an aerofoil in transonic flow by moving the aerofoil from a regime of non-periodic flow to a regime where periodic flow does occur by withdrawal of a trailing-edge splitter plate. The results indicate that the shock induced separation plays a leading role in the origin of shock oscillations.

Computational Investigation of Wing Flutter

Numerical aeroelastic simulation of a high-aspect-ratio transport type wing model in transonic region is presented. The aeroelastic responses of the wing are extracted by integrating compressible thin-layer Navier-Stokes equations coupled with the equations of motion of the wing structure, in a time dependent manner. The Yee-Harten implicit TVD scheme and the Wilson's θ method are employed to integrate these equations, respectively. Flutter boundaries were found for Mach number range, 0.7 to 0.85 and the results were compared with experimental flutter boundaries. Futhermore, Limit Cycle Oscillations were found and the characteristics of the flutter and limit cycle oscillations are investigated and discussed.

A multigrid Navier-Stokes CFD code for rotor computations

This paper presents the development of a multigrid Navier-Stokes code TLNS3DR for rotary wing calculations. The TLNS3DR is developed from the fixed-wing TLNS3D code by including a rotation term and making necessary modifications on boundary conditions. The TLNS3D code solves the thin-layer Navier-Stokes equations using an explicit multistage Runge-Kutta type of time stepping with multigrid method. The TLNS3DR code reformulates the TLNS3D code in the rotor blade-fixed moving frame of reference and solves relative motion of fluids. In this paper, the formulation of the Navier-Stokes equations in the moving frame of reference in terms of relative velocity is given. Several numerical examples are then presented. The results of rotor blade in hover calculated by the new TLNS3DR code seem quantitative correct. The computation also shows that this multigrid code is efficient.

A Computational Fluid Dynamics and Heat Transfer Model for Gaseous Core and Very High Temperature Gas-Cooled Reactors

A computational approach to the solution of Navier-Stokes equations for the thermal and flow fields of very high temperature gas-cooled and gaseous core reactors is presented. An implicit-explicit, finite volume, MacCormack method, in conjunction with the Gauss-Seidel line iteration procedure, is utilized to solve axisymmetric, thin-layer Navier-Stokes equations. An enthalpy rebalancing scheme is implemented to allow the convergence solutions to be obtained with the application of a wall heat flux. The subsonic and supersonic flows of helium in a very high temperature gas-cooled reactor and uranium tetrafluoride (UF4) in a gaseous core reactor under variable boundary conditions (such as adiabatic, isothermal, and constant heat flux) are calculated. The numerical results are compared with other published results and experimental-based correlations. The good agreement with empirical correlations indicates the usefulness of the presented model for the prediction of the flow and temperature distribution under the convective and radiative heat transfer environment of very high temperature gas-cooled and gaseous core reactors.

Artificial Dissipation Schemes for Viscous Airfoil Computations

We examine the effect of the artificial dissipation scheme on the prediction of lift and drag in thin-layer Navier-Stokes computations of subsonic and transonic airfoil flows