The characteristic boundary condition in pressure-based methods

Abstract

This article deals with the implementation of the characteristic boundary condition, also known as the pressure far field boundary condition, in segregated pressure-based flow solvers. This boundary condition applies the Riemann invariants to determine the flow variables at domain inlets and outlets. The newly developed method is implemented in a cell-centered unstructured grid code following a finite volume discretization. Testing is performed by solving the following problems: turbulent flow over a flat plate; inviscid transonic flow over a circular are bump; inviscid supersonic flow over three equidistant circular arc bumps; turbulent flow over an axisymmetric transonic bump; turbulent flow over a NACA 0012 airfoil at 10° angle of attack; and turbulent flow over the three-dimensional ONERA M6 wing at 3.06° angle of attack. Predictions with the current pressure-based solver are compared with similar ones generated using a density-based method and with experimental data. Results are in excellent agreement.     

Numerical study of the wake induced by a porous disk under deflected inflow

This study examines the wake of a porous disk that generates a velocity deficit equivalent to that of a wind turbine. Three-dimensional unsteady numerical simulations based on the finite volume method are performed. The URANS-SST (k–ω) model is applied for the turbulence closure. Two investigations are carried out in this study: (i) the influence of the disk porosity on the wake, for porosities values (p) ranging from 0 to 0.55 in the case of a perpendicular flow; and (ii) the influence of the yaw angle on the wake deviation, for yaw angles ranging from 5° to 30°. Good agreements with the available experimental data are obtained for the mean x-velocity component. The results confirm that wake length increases as porosity decreases. For nonporous disks, most part of the fluid is deflected toward the mast and above the disk. The y-velocity contours highlight two contra-rotating vortices in the vicinity of the disk. In both cases (nonporous and porous disks), a high turbulent kinetic energy is obtained near the disk area, with a higher maximum value for the nonporous disk.     

Simulation of Swirling Turbulent Heat Transfer in a Vortex Heat Exchanger

ABSTRACT

This article presents a numerical simulation of swirling turbulent flow and heat transfer in a novel vortex heat exchanger. A new algebraic Reynolds stress/heat flux model (ASM/AFM) is applied to the simulation. The computation is performed under different air flow rates for both swirling and nonswirling flows. The calculated mean heat transfer coefficients on both inner and outer walls of the annular duct are compared with the measured data. They are generally improved over the results predicted by the new ASM/k–? model. The effects of swirl on enhancing heat transfer in the annular duct are illustrated. The heat transfer performance of the vortex heat exchanger under different air flow rates is obtained.     

Interaction of Surface Radiation With Laminar and Turbulent Natural Convection in Tall Vertical Cavities: Analysis and Heat Transfer Correlations

The interaction of surface radiation with laminar and turbulent natural convection in differentially heated vertical cavities, filled with air and of large aspect ratio (greater than 10), is analyzed in this study. The k ? ωSST turbulence model is used for the formulation of the convection fluid flow and heat transfer, while the governing equations are discretized by the finite-volume method. As an extension of the scarce previous studies, more realistic conditions with a wide range of parameters are considered in the performed simulations. The presented results show the effect of surface radiation on streamlines, isotherms, turbulent kinetic energy, and temperature and vertical velocity profiles, as well as on local and on average convective and radiative heat transfer. Globally, it is found that surface radiation has a weak effect on the dynamic and thermal fields in the major part of the cavity; however, some influence in the upper and lower zones of the cavity is observed. For design purposes, accurate correlations are developed for average convective and radiative Nusselt numbers that cover emissivity of surfaces between 0 and 1, cold wall temperature ranging from 263 K to 303 K, temperature difference between vertical walls ranging from 5 K to 40 K, width of the cavity between 2.5 cm and 7.5 cm, and height of the cavity between 0.25 m and 6 m (this leads to a Rayleigh number ranging from 10³ to 2 × 10⁶ and an aspect ratio between 10 and 80).     

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.     

Effect of chamfering on heat transfer and friction characteristics of solar air heater having absorber plate roughened with compound turbulators

Artificial roughness in the form of repeated transverse chamfered rib-groove roughness on one broad wall has been proposed as a convenient method for enhancement of thermal performance of solar air heater. An experimental investigation on heat and fluid flow characteristics of fully developed turbulent flow in a rectangular duct having repeated integral transverse chamfered rib-groove roughness on one broad wall has been carried out. The roughened wall is uniformly heated while the remaining three walls are insulated. These boundary conditions correspond closely to those found in solar air heaters. Six roughened plates have been tested placing a 60° V-groove at the centre line in between two consecutive chamfered ribs. The ribs' top have been chamfered having chamfer angles of 5°, 12°, 15°, 18°, 22° and 30°, while relative roughness pitch (P/e) and relative roughness height (e/D_h) of the ribs were kept constant having values of 10 and 0.03 respectively. The flow Reynolds number of the duct varied in the range of approximately 3000–21,000, most suitable for solar air heater. The effects of chamfer angle on Nusselt number and friction factor have been discussed and the results are compared with the square rib-grooved and smooth duct under similar flow conditions to investigate the enhancement in Nusselt number and friction factor. The conditions for the maximum enhancement of Nusselt number and friction factor have been determined. It has been found that the thermo-hydraulic performance of the solar air heater provided with such roughness is considerably enhanced.     

NUMERICAL SIMULATIONS ON THE HYDRODYNAMICS OF A TURBULENT SLOT JET IMPINGING ON A SEMICYLINDRICAL CONVEX SURFACE

This study presents the numerical simulations of flow characteristics of a turbulent slot jet impinging on a semicylindrical convex surface. The turbulent-governing equations are solved by a control-volume-based finite difference method with power-law scheme, and the well-known k  ? ε turbulence model associated with the wall function is used to describe the turbulent behavior and structure.

While the width of the slot nozzle is fixed at 9.38 mm, the diameter of the semicylinder is at 150 mm, and air is the working medium, the adopted modifying parameters here include the Reynolds number of the inlet flow (Re = 6000 ~ 20000), jet to impingement surface spacing (y / w = 7 ~ 13), and the entrainment or wall boundary is employed nearby the convex surface. The numerical simulations of flow fields indicate that the velocity distribution of the free jet region departs from the center with increasing y / w. When we increase Reynolds number Re, the variation of the velocity on the convex surface becomes rapid, and the turbulent kinetic energy increases.     

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.     

A Quasi-Implicit Time-Advancing Scheme for Flow in a Three-Dimensional Curved Duct

A quasi-implicit time-marching scheme for solving unsteady incompressible three-dimensional flows on cell-centered unstructured meshes is developed. The finite-volume formulation is used for the spatial derivatives, and the flow variables at the cell face are obtained using the pressure correction. The nonlinear equations resulting from the fully implicit scheme are linearized without deterioration of the overall super-linear time accuracy. The system matrices are solved using the CG iterative method, known as the P-BiCGSTAB method for the momentum equation and the P-CG method for the pressure Poisson equation. The model is applied to simulate fully developed laminar flow in both a 90° curved 3-D circular duct and a 90° curved 3-D square duct. Steady solution is obtained in an unsteady time-marching manner. Computed results compare well with experimental data and other numerical results. It is demonstrated that the present method can be applied to unsteady incompressible laminar 3-D flow with a complex geometry on the unstructured grid system.     

Numerical heat transfer study of turbulent square-duct flow through inline V-shaped discrete ribs

A numerical work has been conducted to examine turbulent periodic flow and heat transfer characteristics in a three dimensional square-duct with inline 60° V-shaped discrete thin ribs placed on two opposite heated walls. The isothermal-flux condition is applied only to the upper and lower duct walls while the two sidewalls are insulated, similar to internal passage cooling of gas turbine blades. The computations are based on the finite volume method with the SIMPLE algorithm for handling the pressure–velocity coupling. Air is the working fluid with the flow rate in terms of Reynolds numbers ranging from 10,000 to 25,000. The numerical result is validated with available square-rib measured data and found to agree well with measurement. The computation reveals that the ribbed duct flow is fully developed periodic flow and heat transfer profiles at about x/D = 7–11 downstream of the inlet. Effects of different rib height to duct diameter ratios, BR, on thermal characteristics for a periodic ribbed duct flow are investigated. It is found that a pair of counter-rotating vortices (P-vortex) caused by the rib can induce impingement/attachment flows on the walls leading to greater increase in heat transfer over the test duct. In addition, the rise of BR values leads to the increase in heat transfer and friction loss. The maximum thermal performance is around 1.8 for the rib with BR = 0.0725 where the heat transfer rate is about 4.0 times above the smooth duct at lower Reynolds number.     

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.     

The Flow Resistance and Heat Transfer Characteristics of Micro Pin-Fins with Different Cross-Sectional Shapes

The flow resistance and heat transfer characteristics of deionized water flowing through a rectangular channel (60 mm × 5.2 mm × 0.5 mm) with staggered array micro pin-fin circular, diamond, and elliptical groups are experimentally investigated over Reynolds numbers ranging from 8 to 1,000, and the investigation shows that the flow resistance increases due to the endwall effect and large pin-fins density at low Re. With the increase in Re, the endwall effect is weakened, but the flow resistance still increases due to the appearance of vortex resistance, and the heat transfer is enhanced due to the flow disturbance or transition from laminar flow to turbulent flow. The experimental results are also compared with predictions of the theoretical correlations for the staggered array micro pin-fin groups, and the comparisons indicate that only the correlation related to the diamond shaped micro pin-fin groups approximately agrees with experimental data, and the other correlations do not describe well the flow and heat transfer characteristics covering laminar, transitional, and turbulent states in circular and elliptical test sections.     

Heat transfer enhancement in a parallel plate duct by an oscillating thin plate insertion

Various arrangements were considered for two thin plates, oscillated by a flow in a parallel plate duct, with a view to enhancing the heat transfer along the duct. Heat transfer and pressure distributions were measured at varying the clearances from the wall and various plate separations. The maximum and mean Nusselt numbers have a Reynolds number dependence of Re^0.8, and were, respectively, 2.3 and 1.6 times as large as those in fully developed turbulent flow, for air with Reynolds number ranging from 9,000 to 37,500. Full-field infrared imaging, a relatively new technique, was used to obtain the temporal and spatial temperature profiles on the wall surface. Isotherm contours of the infrared images correspond well to the heat transfer characteristics and flow. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25 (8): 554–567, 1996     

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.     

Three dimensional simulation of the effects of plasma actuator with radial arrangement of electrodes

Abstract

The purpose of this article is using plasma actuator with special arrangement of electrodes to control flow separation. For this reason, a computational study is carried out on an unsteady, turbulent, and developing flow within a circular duct. The three phenomena including the cross-sectional increase, the developing flow and both tangential and radial simultaneous flow movement determine the physics of the problem. Due to the geometry, the electrodes for the first time are radially arranged.

The results showed that presence of a plasma actuator transferred the separation point from r?=?246.6?mm to r?=?239.2?mm in radial direction. In addition, it was shown that the arrangement of electrodes in the flow direction does not play a role in separation point in radial direction.     

Local convective heat exchanges from a rotor facing a stator

The local convective heat transfer from a rotor with a 310 mm outer radius is studied experimentally at a distance of 3 mm from a coaxial crown-shaped stator with a 176 mm inner radius and a 284 mm outer radius. The experimental technique is based on the use of a thermally thick rotor heated from behind by infrared radiation. The local heat flux distribution from the rotor surface is identified by resolving the Laplace equation by finite difference method using the experimental temperature distribution as boundary conditions. The tests are carried out with the single rotor and the stator/rotor system for local rotational Reynolds numbers ranging from 2.0·10⁴ to 1.47·10⁶ and thus sweeping across the laminar, transition and turbulent flow regimes. The local and mean Nusselt numbers for the single disc are compared with those obtained experimentally for the stator/rotor system. The flow structure in the space between the rotor and the stator is analysed by Particule Image Velocimetry.     

EFFECT OF REYNOLDS AND PRANDTL NUMBERS ON TURBULENT CONVECTIVE HEAT TRANSFER IN A THREE-DIMENSIONAL SQUARE DUCT

Abstract

This paper presents the numerical prediction of thermal developing processes in a square cross-section duct for turbulent flow with isothermal walls. The algebraic stress model has been employed to predict the fully developed turbulent flow. This fully developed turbulent flow was numerically solved using the Teach Program. The three-dimensional energy equation was discretized and solved by the method of lines. According to this method, the energy equation is reformulated by a system of first-order differential equations control-ting the temperature along each line. A nonuniform grid of 8 × 8 nodes was used for calculating the temperature profile at each cross section. The effects of Prandtl and Reynolds numbers on the thermal behavior in the entrance region are investigated. The computed results for the fully developed region are shown to be in good agreement with the measured data publisked in the open literature     

Forced Convective Heat Transfer and Pressure Drop of Air Flowing in a Rectangle Duct with Cross-Ribs on the Opposite Walls

Experiments were conducted to investigate the forced convective heat transfer and flow friction of turbulent airflow in a rectangular duct with cross-ribs attached at the two principal walls in the Reynolds number range from 5000 to 40000. The effect of the rib cross angle (45° 60° 75° and the height (4 mm, 5 mm) of the cross-ribs on the forced convection and flow friction were tested. Non-dimensional correlations for the duct average Nusselt number and friction factor of cross-ribs duct were developed from the test data. Experiments were also conducted for the corresponding parallel ribs to compare their relative performance. The experimental results show that both of the convective heat transfer coefficient and friction factor were increased with cross-ribs, with 45°cross-ribs being the best. Compared with parallel ribs normal to the flow direction under identical flow rate and identical pumping power constraints, the cross-ribs can enhance heat transfer in the lower Reynolds number region, while i     

Experimental investigation on heat-transfer enhancement due to a gap in an inclined continuous rib arrangement in a rectangular duct of solar air heater

Artificial roughness in the form of repeated ribs has been proposed as a convenient method for enhancement of thermal performance of solar air heaters. This paper presents the experimental investigation of heat transfer and friction factor characteristics of a rectangular duct roughened with repeated square cross-section split-rib with a gap, on one broad wall arranged at an inclination with respect to the flow direction. The duct has a width to height ratio (W/H) of 5.84, relative roughness pitch (P/e) of 10, relative roughness height (e/D_h) of 0.0377, and angle of attack (α) of 60°. The gap width (g/e) and gap position (d/W) were varied in the range of 0.5–2 and 0.1667–0.667, respectively. The heat transfer and friction characteristics of this roughened duct have been compared with those of the smooth duct under similar flow condition. The effect of gap position and gap width has been investigated for the range of flow Reynolds numbers from 3000 to 18,000. The maximum enhancement in Nusselt number and friction factor is observed to be 2.59 and 2.87 times of that of the smooth duct, respectively. The thermo-hydraulic performance parameter is found to be the maximum for the relative gap width of 1.0 and the relative gap position of 0.25.     

NUMERICAL SIMULATION OF TURBULENT FLOW IN SMALL-ANGLE DIFFUSERS AND CONTRACTIONS USING A NEW WALL TREATMENT AND A LINEAR HIGH REYNOLDS k–ε MODEL

This work presents numerical prediction for the turbulent flow field confined in a circular duct past a segment of gradually varying cross section. Both expanding and contracting sections are investigated. Equations of boundary-layer type are used and the linear k–ε model, in its high Reynolds form, is applied. A new correlation for treating the grid point closest to the wall is proposed. A marching-forward method is employed for sweeping the computational domain. Computations are first performed for developing and fully developed constant-area ducts in order to assess the reliability of the code. Results are then presented for contractions and diffusers, where comparisons with experimental data for air and water are carried out. Turbulence damping in contractions and its enhancement in diffusers are calculated correctly. Further, for contractions with angles of up to 21°, the use of a parabolic solver shows good agreement with experimental values for the mean and statistical quantities. For diffusers, adverse pressure gradient along the flow limits the quality of the predictions as the angle and length of diffuser increase past 5° and 10 duct radii, respectively.