An implicit implementation of the characteristic boundary condition in a fully coupled pressure-based flow solver

Abstract

The article deals with an implicit formulation of the pressure far field boundary condition, also known as the characteristic boundary condition, in a pressure-based coupled solver. This boundary condition applies to compressible flows over the entire Mach regime, and is derived by invoking the Riemann invariants to implicitly express the flow variables at inlets and outlets in terms of their values inside the domain. A set of inviscid an turbulent flow cases that include pressure far field boundary conditions are tested, namely: low subsonic compressible flow past a NACA0012 airfoil at 10° angle of attack; transonic flow over circular bump; supersonic flow over a series of slender bumps; and DLR-F6 Wing-Body-Nacelle-Pylon Aircraft. Predictions using the prescribed coupled solver are in good agreement with similar results obtained with density-based methods and/or experimental data.     

Effects of the pocket cavity on heat transfer and fluid flow of the downstream outlet guide vane at different flow attacking angles

Abstract

A pocket cavity is generated at the junction position of the low pressure turbine (LPT) and the outlet guide vane (OGV) in the rear part of a modern gas turbine jet engine. In the present study, a triangular pocket cavity is placed upstream of an OGV at different distances. The effects of the pocket cavity on heat transfer and fluid flow of the downstream OGV with different flow attack angles are investigated numerically with well validated turbulence models. The flow attack angles are varied as –30°, 0°, and +30° at a constant Reynolds number =160,000. The turbulent flow details are provided by numerical calculations using two turbulence models, the unsteady DES model and the steady k-ω SST model. For different flow attack angles, the high Nusselt number regions around the OGV are changed. The high heat transfer region is really drawn back at a flow attack angle?=?+30° (Case 2b) compared with Case 2a with a flow attack angle =0°. As the flow attack angle is changed to –30° (Case 2c), the high Nusselt number regions are greatly enlarged not only on the suction side also on the pressure side because of the strengthened flow impingement on the vane surfaces. The pocket cavity weakens the flow impingement on the vane surfaces and the effect is more obvious when the pocket cavity is placed close to the vane. In addition, the heat transfer distribution over the pocket surface is also affected by the location of the vane. When the vane is placed close to the pocket cavity (Case 1), the heat transfer on the pocket edge is increased. In the case with a flow attack angle =0°, the high turbulent kinetic energy region is mainly located near the vane and wake region downstream the vane and recirculating flows can hardly be found.     

Hybrid central–WENO scheme for the large eddy simulation of turbulent flows with shocks

To provide an effective numerical method for the large eddy simulation (LES) of turbulent flows with shocks, a hybrid scheme is developed in a finite volume framework based on the fourth-order central scheme and the third-order weighted essentially non-oscillatory (WENO) scheme. A total of six easy-to-implement and promising switch functions (SFs) are examined in the hybrid central–WENO scheme for the LES of compressible turbulent flows. Both the dissipation and dispersion of the developed hybrid central–WENO scheme are theoretically confirmed using the Fourier technique. Then, the effectiveness and accuracy of this scheme and the SFs are numerically tested by three problems: decaying compressible isotropic turbulence, inviscid, and turbulent transonic flow over a bump. The numerical results show the developed hybrid scheme, coupled with the SF based on local velocity divergence and pressure gradient, has excellent capabilities of capturing shocks and resolving turbulence.     

Thermal performance criteria of elliptic tube bundle in crossflow

In this work, the thermofluid characteristics of the elliptic tube bundle in crossflow have been investigated. Experimental and numerical investigations of the turbulent flow through bundle of elliptic tubes heat exchanger are carried out with a particular reference to the circular tube bundle. The investigation covers the effects of key design parameters of Reynolds numbers (5600–40,000), minor-to-major axis ratios (0.25, 0.33. 0.5 and 1) and flow angles of attack (0–150°). Five bundles of elliptic tube heat exchangers with different axis ratios were designed and manufactured in staggered manner. Numerical CFD modeling using finite volume discretization method was conducted to predict the system performance extensively. Four methods were presented to resort a metric that expresses the thermal performance criteria of the elliptic tube bundle. The results indicated that, increasing the angle of attack clockwise until 90° enhances the convective heat transfer coefficient considerably. The maximum thermal performance under constraint of a fixed pumping power or a mass flow rate was obtained at a zero angle of attack and the minimum thermal performance occurred at an angle of attack equals 90°. The best thermal performance of the elliptic tube heat exchanger was qualified with the lower values of Reynolds number, axis ratio and angle of attack.     

Appraisal and calibration of the actuator line model for the prediction of turbulent separated wakes

The aim of this study is to further investigate the accuracy and the reliability of the actuator line model (ALM) predictions for turbulent separated wakes. Large eddy simulations (LES) of the flow around a NACA0009 airfoil are performed mimicking the geometry with the immersed boundary method. Results are validated against experiments and used to assess the accuracy of the ALM predictions for the same airfoil, with different values of the spreading parameter and of the reference velocity and for two values of the angle of attack. It is found that the ALM setup recently derived from linearized inviscid analysis leads to accurate results for the lower angle of attack, while at the higher one for which a significant separation of the boundary layer occurs, the ALM requires a different set of model parameters. This calls for a systematic investigation of the sensitivity to the ALM parameters for separated flows, which is carried out herein through a stochastic approach allowing continuous response surfaces to be obtained in the parameter space. The ALM parameters are calibrated against the results obtained with the immersed boundaries. With the calibrated model parameters, the ALM gives good predictions of the velocity and turbulent kinetic energy in the far wake. Finally, the proposed model parameters are used to predict the flow past a different geometry, a flat plate, at high angle of attack. The accuracy of the prediction of the far wake is again good, showing the robustness of the identified setup.     

Convergence angle and dimple shape effects on the heat transfer characteristics in a rotating dimple-pin fin wedge duct

Abstract

A numerical method is employed to study effects of convergence angle and dimple shape on flow structure and heat transfer under a rotating frame. The investigated convergence angles are 0.0°, 6.3°, and 12.7°. The dimple shapes are circular, streamwise-elliptical, and spanwise-elliptical. The rotation number ranges from 0.0 to 0.4. Computed flow structures and heat transfer are compared. Higher rotation number generates better heat transfer in the dimple-pin wedge duct. The rotation direction also affects the flow structure and heat transfer. The spanwise-elliptical dimple shape shows best heat transfer augmentation as it generates the strongest vortex structure and turbulent kinetic energy in the dimples. Larger convergence angles exhibit larger Nusselt numbers and better heat transfer enhancement. Effects of the Coriolis force are considered as this force has favorable effects on enhancing the heat transfer on the surface it acts on.     

基于大涡模拟及实验的压气机叶栅角区分离研究

为了研究叶栅内部的流动特性,以及不同攻角下的角区分离模式,对压气机叶栅流场进行了分析。针对两种攻角条件下的平面叶栅模型,采用瞬态雷诺时均(URANS)以及大涡模拟(LES)湍流模型进行了数值模拟研究,并结合叶栅风洞实验验证了数值模拟结果的准确度。对比研究了零攻角以及10°攻角下的叶栅出口流场,叶栅、端壁表面极限流线,以及角区分离结构。研究结果表明:LES能够较好地对角区、尾迹损失进行预测,但URANS在大攻角下的模拟则与实验偏差较大;零攻角下吸力面出现层流分离泡、转捩以及再附现象,而大攻角下吸力面前缘未出现层流分离,而是直接发生转捩以及再附现象;与零攻角相比,10°攻角下的角区分离在展向范围未发生明显变化,在横向范围有小幅度增加,但吸力面附面层分离导致尾迹范围扩大了接近130%,同时总压损失系数提高了接近135%,即大攻角下的主要损失是由吸力面附面层分离以及尾迹损失带来的,而非角区分离。     

MULTIGRID SOLUTION OF UNSTEADY NAVIER-STOKES EQUATIONS USING A PRESSURE METHOD

Abstract

A multigrid relaxation method is applied to a pressure-based implicit procedure to solve the unsteady, incompressible Navier-Stokes equations. The present multigrid method is a correction scheme according to Brandt. This method is used to solve the scalar matrices resulting from the finite-volume formulation and uses flux averaging as the restriction operator. The accuracy and computational efficiency are demonstrated with a steady-state driven cavity flow and an unsteady flow over a circular cylinder case. The results are compared with single-grid results using the OrthoMin conjugate gradient method and experimental data     

Optimal angle of attack for untwisted blade wind turbine

The numerical simulation of horizontal axis wind turbines (HAWTs) with untwisted blade was performed to determine the optimal angle of attack that produces the highest power output. The numerical solution was carried out by solving conservation equations in a rotating reference frame wherein the blades and grids were fixed in relation to the rotating frame. Computational results of the 12° pitch compare favorably with the field experimental data of The National Renewable Laboratory (USA), for both inviscid and turbulent conditions. Numerical experiments were then conducted by varying the pitch angles and the wind speeds. The power outputs reach maximum at pitch angles: 4.12°, 5.28°, 6.66° and 8.76° for the wind speeds 7.2, 8.0, 9.0 and 10.5 m/s, respectively. The optimal angles of attack were then obtained from the data.     

Numerical thermal‐hydraulic performance investigations in turbulent curved channel flow with horseshoe baffles

A numerical work is performed to investigate the thermal‐hydraulic performance in a curved channel of a journal bearing equipped with oblique horseshoe baffles. Water, a working fluid, is passed through the curved channel at a constant temperature condition of 358 K. The effects of different parameters of baffles, that is, attack angle (α = 45°, 60°, and 90°) and the number of baffles (NB = 9 and 13 baffles), are examined. Influences of design parameters on heat transfer and friction performances are studied and displayed in terms of the Nusselt number, the friction factor, the Nusselt number enhancement ratio, and the thermal‐hydraulic performance factor (THPF). The numerical simulations present the flow structures of the tested channel in terms of velocity, isotherms, turbulent kinetic energy, and vorticity contours. The numerical results reveal that the adopted geometry of the curved channel with baffles yields a significant enhancement of heat transfer rate over the plain channel (without baffles), which is approximately 2.5 to 3.8 times. Also, the results show that the best condition to achieve maximum heat transfer is at angle α = 90°, NB = 13, and Re = 5000, compared with other conditions. Furthermore, the maximum THPF of the curved channel using baffles is 4.4 at the same condition. The results confirmed that the geometry of the baffles inside the curved channel has a remarkable impact on heat transfer improvement, accompanied by a reasonable increase in friction losses.     

A Study of the Vortical Flow over a Delta Wing with a Leading Edge Extension

The present paper describes computational and experimental work on the vortex flow characteristics of a sharp-edged delta wing with a leading edge extension (LEX). Experiment was carried out using a low-speed wind tunnel that has a test section of 3.5 m(W)×2.45 m(H)×8.7 m(L). The angle of attack of the delta wing ranges from 10° to 30°. The free stream velocity is fixed at 20 m/s, which corresponds to Reynolds number of 0.88×106. Computations using the mass-averaged implicit 3D Navier-Stokes equations were applied to predict the complicated vortical flow over the delta wing. The governing equations were discretized in space using a fully implicit finite volume differencing formation. The standard k-e turbulent model was employed to close the governing equations. The present computations predicted the experimented flow field with a good accuracy.     

Heat and mass transfer with condensation in laminar and turbulent boundary layers along a flat plate

An experimental and numerical study of heat and mass transfer in an incompressible boundary layer with condensation over a flat plate is presented. The air-steam flow at atmospheric pressure is saturated; its velocity is smaller than 6 m s⁻¹; the Reynolds number calculated with the abscissa along the plate ranges from 10⁴ to 10⁵ for the laminar boundary layer and from 3 × 10⁵ to 10⁶ for the turbulent one. The temperature différence between the main flow and the cold wall does not exceed 20°C. A finite-difference method is used to calculate the velocity, temperature and concentration fields; the numerical results are in good agreement with experiments for laminar and turbulent boundary layer.     

A COMPARATIVE ASSESSMENT WITHIN A MULTIGRID ENVIRONMENT OF SEGREGATED PRESSURE-BASED ALGORITHMS FOR FLUID FLOW AT ALL SPEEDS

This article deals with the evaluation of six segregated high-resolution pressure-based algorithms, which extend the SIMPLE, SIMPLEC, PISO, SIMPLEX, SIMPLEST, and PRIME algorithms, originally developed for incompressible flow, to compressible flow simulations. The algorithms are implemented within a single grid, a prolongation grid, and a full multigrid method and their performance assessed by solving problems in the subsonic, transonic, supersonic, and hypersonic regimes. This study clearly demonstrates that all algorithms are capable of predicting fluid flow at all speeds and qualify as efficient smoothers in multigrid calculations. In terms of CPU efficiency, there is no global and consistent superiority of any algorithm over the others, even though PRIME and SIMPLEST are generally the most expensive for inviscid flow problems. Moreover, these two algorithms are found to be very unstable in most of the cases tested, requiring considerable upwind bleeding (up to 50%) of the high-resolution scheme to promote convergence. The most stable algorithms are SIMPLEC and SIMPLEX. Moreover, the reduction in computational effort associated with the prolongation grid method reveals the importance of initial guess in segregated solvers. The most efficient method is found to be the full multigrid method, which resulted in a convergence acceleration ratio, in comparison with the single grid method, as high as 18.4.     

A strong viscous–inviscid interaction model for rotating airfoils

Two‐dimensional (2D) and quasi‐three dimensional (3D), steady and unsteady, viscous–inviscid interactive codes capable of predicting the aerodynamic behavior of wind turbine airfoils are presented. The model is based on a viscous–inviscid interaction technique using strong coupling between the viscous and inviscid parts. The inviscid part is modeled by a 2D panel method, and the viscous part is modeled by solving the integral form of the laminar and turbulent boundary‐layer equations with extension for 3D rotational effects. Laminar‐to‐turbulent transition is either forced by employing a boundary‐layer trip or computed using an eⁿ envelope transition method. Validation of the incompressible 2D version of the code is carried out against measurements and other numerical codes for different airfoil geometries at various Reynolds numbers, ranging from 0.9 ? 10⁶ to 8.2 ? 10⁶. In the quasi‐3D version, a parametric study on rotational effects induced by the Coriolis and centrifugal forces in the boundary‐layer equations shows that the effects of rotation are to decrease the growth of the boundary‐layer and delay the onset of separation, hence increasing the lift coefficient slightly while decreasing the drag coefficient. Copyright © 2013 John Wiley & Sons, Ltd.     

CFD modelling of laminar‐turbulent transition for airfoils and rotors using the γ − model

When predicting the flow over airfoils and rotors, the laminar‐turbulent transition process can be important for the aerodynamic performance. Today, the most widespread approach is to use fully turbulent computations, where the transitional process is ignored and the entire boundary layer on the wings or airfoils is handled by the turbulence model. The correlation based transition model has lately shown promising results, and the present paper describes the effort of deriving the two non‐public empirical correlations of the model to make the model complete. To verify the model it is applied to flow over a flat plate, flow over the S809 and the NACA63‐415 airfoils, flow over a prolate spheroid at zero and thirty degrees angle of attack, and finally to the NREL Phase VI wind turbine rotor for the zero yaw upwind cases from the NREL/NASA Ames wind tunnel test. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical analysis on heat transfer enhancement by longitudinal vortex based on field synergy principle

Three-dimensional numerical simulation results are presented for a fin-and-tube heat transfer surface with vortex generators. The effects of the Reynolds number (from 800 to 2 000) and the attack angle (30° and 45°) of a delta winglet vortex generator are examined. The numerical results are analyzed on the basis of the field synergy principle to explain the inherent mechanism of heat transfer enhancement by longitudinal vortex. The secondary flow generated by the vortex generators causes the reduction of the intersection angle between the velocity and fluid temperature gradients. In addition, the computational evaluations indicate that the heat transfer enhancement of delta winglet pairs for an aligned tube bank fin-and-tube surface is more significant than that for a staggered tube bank fin-and-tube surface. The heat transfer enhancement of the delta winglet pairs with an attack angle of 45° is larger than that with an angle of 30°. The delta winglet pair with an attack angle of 45° leads to an increase in pressure drop, while the delta winglet pair with the 30° angle results in a slight decrease. The heat transfer enhancement under identical pumping power condition for the attack angle of 30° is larger than that for the attack angle of 45° either for staggered or for aligned tube bank arrangement. Translated from Journal of Xi’an Jiao Tong University, 2006, 40(7): 757–761 [译自: 西安交通大学学报]     

Numerical investigation on heat transfer of supercritical water in a roughened tube

ABSTRACT

The turbulent mixed convection heat transfer of supercritical water flowing in a vertical tube roughened by V-shaped grooves has been numerically investigated in this paper. The turbulent supercritical water flow characteristics within different grooves are obtained using a validated low-Reynolds number κ-ε turbulence model. The effects of groove angle, groove depth, groove pitch-to-depth ratio, and thermophysical properties on turbulent flow and heat transfer of supercritical water are discussed. The results show that a groove angle γ = 120° presents the best heat transfer performance among the three groove angles. The lower groove depth and higher groove pitch-to-depth ratio suppress the enhancement of heat transfer. Heat transfer performance is significantly decreased due to the strong buoyancy force at T_b = 650.6 K, and heat transfer deterioration occurs in the roughened tube with γ = 120°, e = 0.5 mm, and p/e = 8 in the present simulation. The results also show that the rapid variation in the supercritical water property in the region near the pseudo-critical temperature results in a significant enhancement of heat transfer performance.     

Transonic moist air flow around a circular arc blade with bump

The unsteady phenomena in the transonic flow around airfoils are observed in the flow field of fan, compressor blades and butterfly valves, and this causes often serious problems such as aeroacoustic noise and the vibration. In recent years, the effect of bump wall on the flow field around an airfoil has been investigated experimentally and as a result, it was observed that the bump wall is effective for the control of shock wave on the airfoil. In the transonic or supersonic flow field, a rapid expansion of moist air or steam gives rise to non-equilibrium condensation. In the present study, the effect of non-equilibrium condensation of moist air on the self-excited shock wave oscillation around a circular arc blade with or without a bump on the blade was investigated numerically. The results showed that the non-equilibrium condensation significantly reduced the flow field unsteadiness such as root mean of pressure oscillation and frequency compared to the case without the non-equilibrium condensation.     

Implementation of boundary conditions in the finite-volume pressure-based method—Part I: Segregated solvers

ABSTRACT

The paper deals with the formulation of a variety of boundary conditions for incompressible and compressible flows in the context of the segregated pressure-based unstructured finite volume method. The focus is on the derivation and the implementation of these boundary conditions and their relation to the various physical boundaries and geometric constraints. While a variety of boundary conditions apply at any of the physical boundaries (inlets, outlets, and walls), geometric constraints define the type of boundary condition to be used. The emphasis is on relating the mathematical derivation of the boundary conditions to the algebraic equations defined at each centroid of the boundary elements and their coefficients. All derived boundary conditions are validated through a set of test cases with comparison of computed results to available numerical and/or experimental data.     

A LOCALLY IMPLICIT SCHEME FOR TURBULENT FLOWS ON DYNAMIC MESHES

A locally implicit scheme with an anisotropic dissipation model is developed on dynamic quadrilateral-triangular meshes. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low-Reynolds-number k  ? ε turbulence model are solved to study turbulent flows over vibrating blades with negative interblade phase angle. A treatment of viscous flux on quadrilateral-triangular mesh is also presented. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, the turbulent flow around an NACA 0012 airfoil is investigated. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which includes the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady flow behaviors for turbulent flows over vibrating blades with negative interblade phase angle are demonstrated.