Multi-block Grid Research Articles

Numerical study of Transient Flow in a Full-Size Reflected Shock Tunnel

ABSTRACTThe aim of this paper is to develop a CFD solver that used to simulate the transient flow phenomena in a reflected shock tunnel. The transient flow phenomena in a shock tunnel include the reflected shock/boundary layer interaction and the starting process of nozzle flow that can affect the duration of test flow in actual conditions. To numerically simulate these transient flow features, a full-size, axisymmetric reflected shock tunnel model is used. The governing equations are a full Navier-Stokes equation, a species equation and a simplified polynomial correlation to simulate the real gas effects. The numerical code is developed based on the finite volume method coupled with the upwind Roe's scheme and the total variation diminishing (TVD) method. To increase the calculation efficiency, a multi-block and multi-mesh grid generation technique is employed in a huge computational domain. The present computational results have not only confirmed the theoretical characteristics of a shock tube, but have also qualitatively presented the phenomena of reflected shock/boundary layer interaction and the starting process of nozzle flow. This numerical code is a useful tool to demonstrate the actual flow phenomena and to assist the design of experiments.

Three-dimensional flow and heat transfer calculations of film cooling at the leading edge of a symmetrical turbine blade model

Abstract Film cooling of a symmetrical turbine-blade model by lateral and non-lateral injection from one row of holes placed on each side near the leading edge is calculated with a 3D finite-volume method on multi-block grids. For various blowing rates, the flow and temperature fields are predicted, and in particular the contours of film-cooling effectiveness on the blade surface, which are compared with measurements. Various versions of the k – e turbulence model are employed: the standard model with wall functions (WF), a two-layer version resolving the viscous sublayer with a one-equation model and an anisotropy correction due to Bergeles et al. [Num. Heat Transfer 1 (1978) 217–242] which acts to promote the lateral turbulent exchange. The original Bergeles proposal is modified for application in the viscous sublayer. With the standard model, the lateral spreading of the temperature field is underpredicted, leading to averaged film-cooling effectiveness values that are too low. The situation is improved by using the Bergeles correction, especially when the modified correction is applied with the two-layer model (TLK). This yields effectiveness contours in reasonably good agreement with the measurements, but the laterally averaged effectiveness is not predicted in all cases with good accurary. However, the trend of the various influence parameters is reproduced correctly.

Three-dimensional calculations of the flow field around a turbine blade with film cooling injection near the leading edge

Injection of coolant air from a showerhead injection system at the leading edge of a high pressure turbine blade is investigated using a fully implicit three-dimensional finite-volume method on multi-block grids. For various blowing rates, the calculation results for the velocity and pressure fields and turbulence intensity are compared with available experimental data. The present method yields excellent agreement with the experiments for the isentropic Mach number distributions on the blade surface. The standardk–e turbulence model with wall functions is already capable of capturing the major details of the flow field including the injection-induced secondary-flow vortices, particularly so on the suction side. On the pressure side, however, the lateral jet spreading is under-predicted somewhat together with an exaggeration of the near-wall sink-flow vortices. On this side with convex walls, where turbulence anisotropy is appreciable according to the experiments, overall better predictions were obtained with the anisotropy correction of Bergeles et al. [23] promoting the Reynolds stress in the lateral direction. The correction has no beneficial effect on the suction side with concave walls where the turbulence anisotropy was observed to be much smaller.

THREE-DIMENSIONAL PARALLEL COMPUTATION METHOD FOR NON-UNIFORM PARTICULATE FLOWS

A parallel computation technique has been proposed for mixing and segregation of granular mixture with a multi-block grid system. The particle motions in multiple sub-blocks are calculated simultaneously on the basis of the distinct element method (DEM). The possible particle contacts through the common boundary shared by two sub-blocks are detected by exchanging the particle information included in the near-boundary volumes. The developed computational method was applied to the particulate flows in a cylinder rotating around its horizontal axis. From the comparison of the necessary CPU time, the computational efficiency in the parallel method has been confirmed. In addition, it was shown that the predicted distributions of the granular binary mixture are in good agreement with the experimental results.

Computation of ship transom stern flow using a multiblock grid method

The incompressible Reynolds Averaged Navier-Stokes (RANS) code using the multiblock grid method has been developed for simulating the steady free surface flows over ship having complex geometries. “Horizontal Mode”, “Vertical Mode” and “BJ-SGS” which are methods of updating boundary conditions on block interfaces are incorporated in the present code and investigated in the computation of free surface flows about Wigley hull. The new code is applied to computation of transom stern flow about a container ship and a high speed vessel and those numerical results are compared with the experimental results.

Partitioning strategies for structured multiblock grids

A framework is presented for partitioning of multiblock grids used in data parallel applications. It includes partitioning strategies found in the literature, as well as new algorithms proposed here. In particular, a multilevel graph-partitioning strategy – specifically designed for structured composite grids – is proposed. Different partitioning strategies are compared in two case studies involving multiblock grids. One of the applications is a profile of a multi-element wing from Airbus A310. The partition properties from the different strategies and algorithms depend very much on the number of subgrids and their sizes as well as on the number of processors. Results demonstrate that existing strategies behave well in some cases while the new multilevel graph-partitioning strategy gives an overall good performance.

Numerical simulation of the lateral aerodynamics of an orbital stage at stage separation flow conditions

The unsteady flow of an idealized two-stage hypersonic vehicle during the separation process is investigated. In particular, the aerodynamic characteristics of the orbital stage performing yaw and roll oscillations with defined frequencies at a certain distance above the lower stage are addressed. The numerical simulations of the flowfield are based on an explicit finite-volume method for solutions of the three-dimensional unsteady Euler equations. The discretization of the computational domain around the entire configuration is performed using a flexible multiblock grid generator. The results focus on the flowfields and the pressure distributions as well as on the aerodynamic coefficients. The latter provide an essential mean for the stability and control evaluations for lateral motion in hypersonic flight. The analysis show that unsteadiness cannot be neglected.

Heat transfer on a film-cooled rotating blade

Abstract A multi-block, three-dimensional Navier–Stokes code has been used to compute heat transfer coefficient on the blade, hub and shroud for a rotating high-pressure turbine blade with 172 film-cooling holes in eight rows. Film-cooling effectiveness is also computed on the adiabatic blade. Wilcox's k – ω model is used for modeling the turbulence. Of the eight rows of holes, three are staggered on the shower-head with compound-angled holes. The multi-block grid consists of 4818 elementary blocks which were merged into 280 super blocks. The viscous grid has nearly two million cells. Each hole-exit, in its true oval shape, has 80 cells within it so that coolant velocity, temperature, k and ω distributions can be specified at these hole-exits. For the given parameters, heat transfer coefficient on the cooled, isothermal blade is found to be high in the tip region, and in the leading edge region between the hub and blade mid-span. The effectiveness over the cooled, adiabatic blade is the lowest in these regions. Results for an uncooled blade are also shown, providing a direct comparison with those for the cooled blade. The heat transfer coefficient is much higher on the blade tip and shroud as compared to that on the hub for both the cooled and the uncooled cases. Effect of gridding the tip clearance gap vs. use of a tip clearance model, as well as the effect of different orientation of coolant ejection from shower-head holes is found to be small as far as the heat transfer coefficient or the adiabatic effectiveness on the blade surface is concerned.

Alternating Plane Smoothers For Multiblock Grids

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

B211個別要素法による固液混相流の並列計算と数値可視化

A new parallel computational technique has been proposed for the liquid flows including granular mixture with multi-block grid system. In this technique, a three-dimensional computational volume is decomposed into multiple blocks which are represented by 3D body-fitted coordinates. Both of the computations of particle motions with the distinct element method (DEM) and liquid flows with a turbulence model in the multiple blocks are executed simultaneously. The interaction between two phases are take into account on the basis of a two-way method. Since the numerical visualization procedure is also treated as one of the parallel processes, it scarcely affects the efficiency of the other computations. The computational method was applied to the granular binary mixture exposed to the oscillating flows in a pipe. As a result, it was shown that the reasonable transportation of particles is predicted and that the segregation of the granular mixture is qualitatively predicted.

Multi-block mesh extrusion driven by a globally elliptic system

This paper investigates the possibility of using a boundary integral equation to facilitate the generation of multi-block grid systems about semi-complex geometries. The integral equation utilized is that for a source density distribution over the surface of the body about which the conforming grid system is sought. Advantages of and restrictions to the current method are discussed in relation with other gridding techniques. Sample grid systems are provided for several dissimilar geometric shapes which illustrate the quality and robustness of the present scheme. Copyright © 2000 John Wiley & Sons, Ltd.

Mixed Finite Element Methods on Nonmatching Multiblock Grids

We consider mixed finite element methods for second order elliptic equations on nonmatching multiblock grids. A mortar finite element space is introduced on the nonmatching interfaces. We approximate in this mortar space the trace of the solution, and we impose weakly a continuity of flux condition. A standard mixed finite element method is used within the blocks. Optimal order convergence is shown for both the solution and its flux. Moreover, at certain discrete points, superconvergence is obtained for the solution and also for the flux in special cases. Computational results using an efficient parallel domain decomposition algorithm are presented in confirmation of the theory.

Numerical Analysis of Three-Dimensional Flow in a Forward Curved Centrifugal Fan

Numerical study of three-dimensional turbulent flow in a forward curved centrifugal fan is presented. Standard turbulence model and non-orthogonal curvilinear coordinates arc used to consider the turbulent flow field and complex geometry. Finite Volume approach is adopted for discretization scheme and structured grid system is used to help convergence. Multiblock grid system is used for flow field and divided into five domains that are inlet, outlet, impeller, tip clearance and scroll. It is assumed that the flow field is steady and incompressible. These numerical results are compared with the experimental data inside a rotor and at the fan outlet. Most important flow features are captured through this numerical approach. Finally details of flow field inside a fan are described and analyzed.

Multi-Block Large-Eddy Simulations of Turbulent Boundary Layers

Time-developing turbulent boundary layers over an isothermal flat plate at free-stream Mach numbers of 0.3 and 0.7 are computed using an explicit finite-difference method on structured multi-block grids. The size of each block is adjusted depending on the dimension of the largest structures present locally in the flow. This alleviates the cost of calculations in which the wall layer is resolved, and may result in substantial savings of memory and CPU time, if several layers are used. In the calculations presented the near-wall region is computed using a domain with a spanwise length L+o=820, which is sufficient to contain several streaks. This grid block is repeated periodically in the spanwise direction. The outer layer, which contains larger structures, is computed using a domain that is twice as wide (L+o=1640). Although the flow at the interface between the blocks has a periodicity length determined by the inner-layer block, within a few grid points longer wavelengths are generated. The velocity statistics and rms intensities compare well with single-block calculations that use substantially more grid points.

Numerical multi-block grids in coastal ocean circulation modeling

In coastal ocean modeling, one desires to capture the evolution and interaction of multi-scales of physical phenomena in a complicated physical domain. With limited computer resources, an appropriate choice of the numerical grid has a key role in determining the quality of the solution of a numerical coastal ocean model. Traditionally, single-block rectangular grids have been most commonly used in coastal ocean modeling for their simplicity. An effective coastal ocean model represents the dynamics of the coastal ocean flow on a numerical grid, including the effects of complicated features such as coastlines, bottom topography (submarine canyons, seamounts, narrow straits), and multi-scale physical phenomena. These problems require a model grid system more efficient than a traditional single-block rectangular grid. The model grids must give better resolution of coastlines and boundary conditions, multi-scale physical phenomenon, and save computer resources. These grids can also easily increase horizontal resolution in a subregion of the model domain without increasing computer expense with high resolution over the entire domain. The multi-block numerical generation grid technique is used in developing a coastal ocean system applied to the Mediterranean Sea (MED) with complicated coastlines, bottom topography and multi-scale physical features. The MED coastal ocean system consists of the MED model based on the Princeton Ocean Model, numerical grid generation routines, and a grid package which allows the model to be coupled with model grids. The traditional, nine-block orthogonal grid, and eight-block curvilinear nearly orthogonal coastline-following grid are used in the study. The numerical solutions with the three grids are compared in term of effectiveness. The numerical simulations show some MED basic physical features.

A unified-grid finite volume formulation for computational fluid dynamics

A new extremely flexible finite volume framework is presented. It is based on updating cell average values of the dependent variables. It is embedded in a unified-grid framework that unifies the treatment of structured and unstructured grids, single and multi-block grids, patched-aligned, patched-non-aligned and overset grids, and various cell shapes, including hexahedra, triangular prisms and tetrahedra in three dimensions, quadrilaterals and triangles in two dimensions and the linear element in one dimension. A novel discretization approach has been developed to deal with unified-grid topologies. It includes a piecewise-linear multi-dimensional non-oscillatory reconstruction procedure that is based on synergistic utilization of polynomials at cell vertices. Least-squares reconstruction is used when necessary. The concept of generalized neighborhoods is introduced to account for cell neighborhoods that include cells that are not logically connected through common nodes, faces, etc. This helps in the automatic treatment of all types of multi-block meshes. To go with such a general discretization procedure, new implicit relaxation procedures are introduced that help achieve fast convergence to steady state solutions. The framework has been implemented in a new CFD code (CFD++) using a finite volume formulation. The paper presents the methodology with the help of several annotated examples taken from various compressible and incompressible flows. Copyright © 1999 John Wiley & Sons, Ltd.

A Numerical Simulation of Hydrocyclones

A numerical method is presented for the calculation of the three-dimensional flow and separation efficiency for particles with low concentrations in a hydrocyclone. Multi-block curvilinear grids in the frame of a cylindrical coordinate system are used to represent accurately the hydrocyclone geometry. Turbulence is represented by a modified k — ɛ model which adds a curvature correction term with a single empirical constant in the dissipation equation. Both three- and two-dimensional axisymmetric computations are carried out and are compared with experimental data. It is shown that the standard k — ɛ model can produce large errors which result in incorrect predictions of the flow patterns. The three-dimensional calculations using the modified k — ɛ model produce results in good agreement with experimental data. The two-dimensional axisymmetric calculations can predict approximate flow patterns, but are inadequate to predict the separation efficiency of hydrocyclones. To analyse the separation efficiency, a three-dimensional model, as developed in the present study, is required.

Turbulent Flow Induced by Full-Scale Ship in Harbor

A chimera Reynolds-averaged Navier-Stokes (RANS) method has been developed for time-domain simulation of transient flow induced by a ship approaching a berthing facility. The method solves the mean flow and turbulence quantities on embedded, overlapped, or matched multiblock grids. The unsteady RANS equations were formulated in an earth-fixed reference frame and transformed into general curvilinear, moving coordinate systems. A chimera domain decomposition techniques has been employed to accommodate the relative motions between different grid blocks. Calculations have been performed for a full-scale motor vessel in berthing operations. Comparisons have been made between the computations and measurements to demonstrate the feasibility of the chimera RANS approach for time-domain simulation of the hydrodynamic coupling between the ship and berthing structures. The numerical solutions successfully captured many important features of the transient flow around a berthing ship, including the underkeel flow acceleration, wake flow separation, and water cushioning effects between the ship and harbor quay wall.

Numerical grids used in a coastal ocean model with breaking wave effects

In coastal ocean modeling, traditional single-block rectangular (Cartesian) grids have been most commonly used for their simplicity. In many cases, these grids may be not well suited (even at very high resolutions) for regions with complicated physical fields, open boundaries, coastlines, and bottom bathymetry. The numerical curvilinear nearly orthogonal/orthogonal, single/multi-block coastline-following grids for the Mediterranean Sea, Monterey Bay and the South China Sea (SCS) are presented. These grids can be used in coastal ocean modeling to enhance model numerical solutions and save computer resources by giving better treatment of regions with high gradients such as areas of complicated coastlines and steep slopes of shelf breaks, complicated bottom topography, open boundaries, and multi-scale physical phenomenon. Grid generation techniques are used to designed these grids. This kind of grids can also easily increase horizontal resolutions in the subregion of the model domain, without increasing the computational expense, with a higher resolution over the entire domain. A three dimensional coastal ocean model with breaking wave effects is also presented and applied. The ocean system is a primitive equation modeling system with grid generation routines and a turbulent closure which is capable of taking surface breaking wave effects into account. The system also includes a grid package which allows model numerical grids to be coupled with the ocean model. The model code is written for multi-block grids, but a single-block grid is used for the South China Sea (SCS). The model with breaking wave effects and a grid of 121 × 121 grid points are used to simulate the winter circulation of the SCS as an example. The model output of the 60-day run shows the observed upwelling locations in the sea surface salinity field.

Heat transfer on a film-cooled blade – effect of hole physics

Abstract A multiblock, three-dimensional Navier–Stokes code has been used to study the within-hole and near-hole physics in relation to heat transfer on a film-cooled blade. The flow domain consists of the coolant flow through the plenum and hole-pipes for the three staggered rows of shower-head holes on the VKI rotor, and the main flow over the blade. A multiblock grid is generated that is nearly orthogonal to the various surfaces. It may be noted that for the VKI rotor the shower-head holes are inclined at 30° to the spanwise direction, and are normal to the streamwise direction on the blade. Wilcox's k–ω turbulence model is used. The present study provides a much better comparison for the span-averaged heat transfer coefficient on the blade surface with the experimental data than an earlier analysis wherein coolant velocity and temperature distributions were specified at the hole exits rather than extending the computational domain into the hole-pipe and plenum. Details of the distributions of coolant velocity, temperature, k and ω at the hole exits are also presented.