| Publications |
These are some of the recent publications of the CFD @AUB group. They are grouped into Journal Papers, Conference Papers and Reports.
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| Journal Papers |
Mixing and Evaporation of Liquid Droplets Injected
into an Air Stream Flowing at all Speeds
(PDF) Abstract- This paper deals with the formulation, implementation, and testing of three numerical techniques based on (i) a full multiphase approach, (ii) a MUlti-SIze Group (MUSIG) approach, and (iii) a Heterogeneous MUSIG (H-MUSIG) approach for the prediction of mixing and evaporation of liquid droplets injected into a stream of air. The numerical procedures are formulated following an Eulerian approach, within a pressure-based fully conservative Finite Volume method equally applicable in the subsonic, transonic, and supersonic regimes, for the discrete and continuous phases. The k-ε two-equation turbulence model is used to account for the droplet and gas turbulence with modifications to account for compressibility at high speeds. The performances of the various methods are compared by solving for two configurations involving stream-wise and cross-stream spraying into subsonic and supersonic streams. Results, displayed in the form of droplet velocity vectors, contour plots, and axial profiles indicate that solutions obtained by the various techniques exhibit similar behavior. Differences in values are relatively small with the largest being associated with droplet volume fractions and vapor mass fraction in the gas phase. This is attributed to the fact that with MUSIG and H-MUSIG no droplet diameter equation is solved and the diameter of the various droplet phases are held constant, as opposed to the full multiphase approach.
Buoyancy Induced Heat Transfer in a
Trapezoidal Enclosure with Offset Baffles (PDF) Abstract- A numerical study has been conducted to examine the effects on heat transfer of mounting two offset baffles onto the upper inclined and lower horizontal surfaces of trapezoidal cavities. Two thermal boundary conditions are considered. In the first, the left short vertical wall is heated while the right long vertical wall is cooled (buoyancy assisting mode along the upper inclined surface of the cavity). In the second, the right long vertical wall is heated while the left short vertical wall is cooled (buoyancy opposing mode along the upper inclined surface of the cavity). For both boundary conditions, computations are performed for: several offset baffle heights, four Rayleigh number values, three Prandtl (Pr) number values, and two baffle positions (Position I and Position II). In Position I, the lower baffle is offset toward the short vertical wall and the upper baffle is offset toward the long vertical wall of the enclosure, whereas in Position II, the lower and upper baffles are offset toward the long and short vertical walls, respectively. Results reveal a decrease in heat transfer in the presence of baffles with its rate generally increasing with increased baffle height and Pr. At a given baffle height and Ra, Nu values are lower in the buoyancy opposing mode. For both boundary conditions, the highest decrease is achieved in fully partitioned enclosures.
A Coupled Incompressible Flow Solver On
Structured Grids (PDF) Abstract- This paper deals with the formulation, implementation and testing of a fully coupled velocity-pressure algorithm for the solution of laminar incompressible flow problems. The tight velocity-pressure coupling is developed within the context of a collocated structured grid, and the systems of equations involving velocity and pressure are solved simultaneously. The pressure and momentum equations are derived in a way similar to a segregated SIMPLE algorithm [1], yielding an extended set of diagonally dominant equations. An algebraic multigrid solver is used to accelerate the solution of the extended system of equations. The performance of the newly developed coupled algorithm is evaluated by solving three test problems showing the effects of grid size, mesh skewness, large pressure gradients, and large source terms on the convergence behavior. Results are presented in the form of convergence history plots and tabulated values of the maximum number of required iterations, the total CPU time, and the CPU time per control volume. This latter performance indicator is shown to be nearly independent of the grid size.
Convective Schemes for Capturing Interfaces
of Free-Surface Flows on Unstructured Grids (PDF) Abstract- In this paper, the general methodology used in constructing interface capturing schemes is clarified and concisely described. Moreover, a new interface capturing scheme, denoted by STACS, based on a switching strategy is developed. The accuracy of the new scheme is compared to the well known CICSAM and HRIC schemes by solving the following test problems: advection of (i) a hollow square, (ii) a rotated hollow square, (iii) and a hollow circle in an oblique velocity field, and (iv) a slotted circle in a rotating flow field. Results, displayed in the form of interface contours for the various schemes, reveal deterioration in the accuracy of CICSAM and HRIC schemes with their performance approaching that of the UPWIND scheme as the Courant number increases. On the other hand, predictions obtained with the new STACS scheme are by far more accurate and less diffusive preserving interface sharpness and Boundedness at all Courant number values considered.
Pressure Based Algorithms for Multi-Fluid Flow
at all Speeds-Part II: Geometric Conservation Formulation (PDF) Abstract- This work is concerned with the implementation and testing, within a structured collocated finite-volume framework, of seven segregated algorithms for the prediction of multi-phase flow at all speeds. These algorithms belong to the Geometric Conservation Based Algorithms (GCBA) group in which the pressure correction equation is derived from the constraint equation on volume fractions (i.e. sum of volume fractions equals 1). The pressure correction schemes in these algorithms are based on SIMPLE, SIMPLEC, SIMPLEX, SIMPLEM, SIMPLEST, PISO, and PRIME. The performance and accuracy of these algorithms are assessed by solving, using the single grid method (SG), the prolongation grid method (PG), and the full non-linear multi-grid method (FMG), the following four two-dimensional two-phase flow problems: (i) turbulent upward bubbly flow in a pipe, (ii) turbulent air-particle flow in a pipe, (iii) compressible dusty flow over a flat plate, (iv) and transonic dusty flow in a converging-diverging nozzle. Results are displayed in the form of convergence history plots and tabulated CPU times. The main outcomes of this study are the clear demonstrations of: (i) the capability of all GCBA algorithms to deal with multi-fluid flow situations; (ii) the ability of the FMG method to tackle the added non-linearity of multi-fluid flows; (iii) and the capacity of the GCBA algorithms to predict multi-fluid flow at all speeds. Pressure-Based
Algorithms for Multi-Fluid Flow at All Speeds-Part I: Mass Conservation
Formulation (PDF) Abstract-In this paper seven segregated single-fluid pressure-based algorithms are extended to predict multi-fluid flow at all speeds. The extended algorithms form part of the Mass Conservation Based Algorithms (MCBA) group in which the pressure correction equation is derived from overall mass conservation. The performance and accuracy of these algorithms are assessed by solving a variety of two-dimensional two-phase flow problems in the subsonic, transonic, and supersonic regimes. Solutions are generated for several grid densities using the single grid (SG), the prolongation grid (PG), and the full non-linear multi-grid (FMG) methods and their effects on convergence behavior studied. The main outcomes of this study are the clear demonstrations of: (i) the capability of all MCBA algorithms to deal with multi-fluid flow situations; (ii) the ability of the FMG method to tackle the added non-linearity of multi-fluid flows; (iii) and the capacity of the MCBA algorithms to predict multi-fluid flow at all speeds. Moreover, results indicate that the performances of SIMPLE, SIMPLEC, and SIMPLEX are very close. The PRIME algorithm is the most expensive due to the explicit treatment of the fluidic momentum equations. The PISO algorithm is generally more expensive than SIMPLE. In terms of CPU effort SIMPLEM stands between PRIME and SIMPLE. For all algorithms, the use of the PG and FMG methods speed-up acceleration with the FMG method being more efficient accelerating the convergence rate, for the problems solved on the densest grid used, over the SG method by a factor reaching a value as high as 6.55.
Natural
Convection in a Partitioned Trapezoidal Cavity Heated from the Side
(PDF) Abstract-Numerical results are reported for natural convection heat transfer in partially divided trapezoidal cavities representing industrial buildings. Two thermal boundary conditions are considered. In the first, the left short vertical wall is heated while the right long vertical wall is cooled (buoyancy assisting mode along the upper inclined surface of the cavity). In the second, the right long vertical wall is heated while the left short vertical wall is cooled (buoyancy opposing mode along the upper inclined surface of the cavity). The effects of Rayleigh number, Prandtl number, baffle height, and baffle location on the heat transfer are investigated. Results are displayed in terms of streamlines, isotherms, and local and average Nusselt number values. For both boundary conditions, predictions reveal a decrease in heat transfer in the presence of baffles with its rate generally increasing with increasing baffle height and Pr. For a given baffle height, higher decrease in heat transfer is generally obtained with baffles located close to the short vertical wall.
A
Comparative Assessment within a Multi-Grid Environment of Segregated
Pressure-Based Algorithms for Fluid Flow at All Speeds (PDF) Abstract- This paper 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, into 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. The Performance
of Geometric Conservation Based Algorithms for Incompressible Multi-Fluid
Flow (PDF) Abstract- This paper deals with the implementation and testing of seven segregated pressure-based algorithms for the prediction of incompressible multi-fluid flow. These algorithms belong to the Geometric Conservation Based Algorithm (GCBA) group in which the pressure correction equation is derived from the constraint on volume fractions (i.e. sum of volume fractions equals 1). The pressure correction schemes in these algorithms are based on SIMPLE, SIMPLEC, SIMPLEX, SIMPLEM, SIMPLEST, PISO, and PRIME. The performance and accuracy of these algorithms are assessed by solving eight one-dimensional two-phase flow problems and comparing results with published data. The effects of grid size on convergence characteristics are analyzed by solving each problem over different grid sizes. Results clearly demonstrate the capability of all GCBA algorithms to predict a wide range of multi-fluid flow situations. Based on the convergence history plots and CPU-times obtained for the problems solved, the GCBA can be divided into two groups with the one composed of SIMPLEST and PRIME being generally less efficient than the second group to which the remaining algorithms belong. Natural Convection
in a Trapezoidal Enclosure Heated From the Side with a Baffle Mounted
on its Upper Inclined Surface (PDF) Abstract- A numerical investigation has been carried out to examine the effects on heat transfer of mounting baffles to the upper inclined surfaces of trapezoidal cavities. Two thermal boundary conditions are considered. In the first, the left short vertical wall is heated while the right long vertical wall is cooled (buoyancy assisting mode along the upper inclined surface of the cavity). In the second, the right long vertical wall is heated while the left short vertical wall is cooled (buoyancy opposing mode along the upper inclined surface of the cavity). For each boundary condition, computations are performed for three baffle heights, two baffle locations, four Rayleigh number values, and three Prandtl number values. Results are displayed in terms of streamlines, isotherms, and local and average Nusselt number values. For both boundary conditions, predictions reveal a decrease in heat transfer in the presence of baffles with its rate generally increasing with increasing baffle height and Pr. For a given baffle height, higher decrease in heat transfer is generally obtained with baffles located close to the short vertical wall. Average Nusselt number correlations for both boundary conditions are presented. The Schemes:
A New Consistent High-Resolution Formulation Based on the Normalized
Variable Methodology (PDF) Abstract- This paper deals with the formulation and testing of a new class of consistent High-Resolution (HR) schemes, denoted as the -schemes. These schemes, combine consistency, accuracy and boundedness across systems of equations and are suitable for use in the simulation of multi-phase and multi-component flows. The consistency feature refers to the capability of these schemes to implicitly satisfy the additional algebraic constraint representing a global conservation relation governing certain sets of equations (e.g., species mass fraction, volume fraction, etc.). Four schemes are implemented within an unstructured grid finite-volume framework, tested by solving four multi-component pure-advection test problems, and shown to be consistent. A Robust Multi-Grid
Pressure-Based Algorithm for Multi-Phase Flow at All Speeds (PDF) Abstract- A number of approaches have evolved over the last decade for the implementation of TVD schemes within an unstructured grid finite volume method framework. Unfortunately none of these approaches has been comprehensive enough to permit the general implementation of TVD–based schemes in unstructured grids, and/or accurate enough to recover the exact TVD formulation in structured grids. In this paper we propose a simple method that allows the implementation of the full spectrum of TVD schemes in unstructured grids, while recovering their exact formulation on structured grids. Four schemes implemented using this approach, TVD-MINMOD, TVD-MUSCL, TVD-SUPERBEE, TVD-OSHER, are tested and compared to Bruner’s TVD formulation [1], and to the Barth and Jesperson linear reconstruction scheme [2] by solving four pure advection problems. Results indicate that the Bruner formulation yields, for the same original TVD scheme, overly diffusive results when compared to the current method. The BJ-MUSCL and TVD-MUSCL are shown to be comparable and more accurate than the OSHER scheme. The SUPERBEE performs best though showing tendency for stepping the modeled profile. In all tests the current method is found to retain the behavior of the structured grid TVD formulation. A Comparative
Assessment of the Performance of Mass Conservation Based Algorithms
For IncompressibleMulti-Phase flows (PDF) Abstract- This work is concerned with the implementation and testing, within a structured collocated finite-volume framework, of seven incompressible-segregated multi-phase flow algorithms that belong to the Mass Conservation Based Algorithms (MCBA) group in which the pressure correction equation is derived from overall mass conservation. The pressure correction schemes in these algorithms are based on SIMPLE, SIMPLEC, SIMPLEX, SIMPLEM, SIMPLEST, PISO, and PRIME. The performance and accuracy of the multi-phase algorithms are assessed by solving eight one-dimensional two-phase flow problems spanning the spectrum from dilute bubbly to dense gas-solid flows. The main outcome of this study is a clear demonstration of the capability of all MCBA algorithms to deal with multi-phase flow situations. Moreover, results displayed in terms of convergence history plots and CPU-times, indicate that the performances of the MCBA versions of SIMPLE, SIMPLEC, and SIMPLEX are very close. In general, the performance of SIMPLEST approaches that of SIMPLE for diffusion-dominated flows. As expected, the PRIME algorithm is found to be the most expensive due to its explicit treatment of the phasic momentum equations. The PISO algorithm is generally more expensive than SIMPLE and its performance depends on the type of flow and solution method used. The behavior of SIMPLEM is consistent and in terms of CPU effort it stands between PRIME and SIMPLE.
A
Pressure-Based Algorithm for Multi-Phase Flow at all Speeds (PDF) Abstract- A new finite volume-based numerical algorithm
for predicting incompressible and compressible multi-phase
flow phenomena is presented. The technique is equally
applicable in the subsonic, transonic, and supersonic
regimes. The method is formulated on a non-orthogonal
coordinate system in collocated primitive variables.
Pressure is selected as a dependent variable in preference
to density because changes in pressure are significant
at all speeds as opposed to variations in density,
which become very small at low Mach numbers. The pressure
equation is derived from overall mass conservation.
The performance of the new method is assessed by solving
the following two-dimensional two-phase flow problems:
(i) incompressible turbulent bubbly flow in a pipe,
(ii) incompressible turbulent air-particle flow in
a pipe, (iii) compressible dilute gas-solid flow over
a flat plate, and (iv) compressible dusty flow in a
converging diverging nozzle. Predictions are shown
to be in excellent agreement with published numerical
and/or experimental data. Abstract- A new collocated finite volume-based solution procedure for predicting viscous compressible and incompressible flows is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regimes. Pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density which become very small at low Mach numbers. The newly developed algorithm has two new features; (i) the use of the Normalized Variable and Space Formulation methodology to bound the convective fluxes; and (ii) the use of a high-resolution scheme in calculating interface density values to enhance the shock capturing property of the algorithm. The virtues of the newly developed method are demonstrated by solving a wide range of flows spanning the subsonic, transonic, and supersonic spectrum. Results obtained indicate higher accuracy when calculating interface density values using a High-Resolution scheme. A Unified Formulation
of the Segregated Class of Algorithms for Multi-Fluid Flow at All
Speeds (PDF) Abstract-The class of segregated pressure-based, single-fluid, all speed flow algorithms is extended to multi-fluid flow simulations using a unified, compact, and easy to understand notation. Depending on the constraint equation used to derive the pressure correction equation, the extended multi-fluid flow algorithms are shown to fall under two categories denoted in this work by the Mass Conservation Based Algorithms (MCBA) and the Geometric Conservation Based Algorithms (GCBA). This paper deals with the formulation of both types of algorithms and presents several techniques developed to promote and accelerate their convergence. Moreover, the differences and similarities between the two categories are explained and the mass conservation-based formulation is shown to represent a subset of the geometric-based formulation A Unified Formulation of the Segregated Class of Algorithms
for Abstract - In this paper, the segregated SIMPLE algorithm and
its variants are reformulated, using a collocated variable
approach, to predict fluid flow at all speeds. In the
formulation, a unified, compact, and easy to understand
notation is employed. The SIMPLE, SIMPLER, SIMPLEST,
SIMPLEM, SIMPLEC, SIMPLEX, PRIME, and PISO algorithms
that are scattered in the literature and appear to
a non-versed CFD user as being unrelated, are shown
to share the same essence in their derivations and
to be equally applicable for the simulation of incompressible
and compressible flows. Moreover, the philosophies
behind these algorithms in addition to their similarities
and differences are explained. Abstract-The indiscriminate application of the Convective Boundedness Criterion (CBC) in all flow regions results in a new and subtle error that leads to a significant reduction in accuracy at locations where physical extrema (maxima or minima) with steep profiles are present. In this paper, a new Bounded EXtremum PREServing Strategy (B-EXPRESS) that addresses this issue is presented. The B-EXPRESS is a two-stage procedure in which, an Extremum Recognition Algorithm (ERA) is first applied to a solution converged to a set level to flag locations at which enforcing the CBC leads to extrema attenuation. Then, in the second stage, an unbounded scheme is used at the flagged locations, while a bounded scheme is used elsewhere. The new strategy is applied to the SMART (a 3rd order bounded scheme) and BSEVENTH (a 7th order bounded scheme) schemes to yield two new schemes denoted by B-EXPRESS-3 and B-EXPRESS-7, respectively. These schemes are tested by solving four problems of pure convection in an oblique velocity field of a sinusoidal, elliptic, triangular, and box profiles. Results obtained reveal the B-EXPRESS-3 to greatly reduce the rate of attenuation in the levels of the profiles and to be as accurate as the BSEVENTH scheme which, on average, requires 540% more CPU time than the B-EXPRESS-3 scheme. Moreover, the B-EXPRESS-7 scheme computations do not show any observable attenuation in the levels of the profiles while marginally increasing the CPU effort (3.43% on average) over the BSEVENTH scheme. A Unified Formulation of the Segregated Class of Algorithms for Fluid Flow at All Speeds (PDF) Numerical Heat Transfer, Part B: Fundamentals, vol 37, No. 1, pp 103-139, 2000. Abstract -In this paper, the segregated
SIMPLE algorithm and its variants are reformulated, using a collocated variable
approach, to predict fluid flow at all speeds. In the formulation, a unified,
compact, and easy to understand notation is employed. The SIMPLE, SIMPLER,
SIMPLEST, SIMPLEM, SIMPLEC, SIMPLEX, PRIME, and PISO algorithms that are scattered
in the literature and appear to a non-versed CFD user as being unrelated, are
shown to share the same essence in their derivations and to be equally applicable
for the simulation of incompressible and compressible flows. Moreover, the
philosophies behind these algorithms in addition to their similarities and
differences are explained. An Efficient Very High-Resolution scheme Based on an Adaptive-Scheme Strategy (PDF) Numerical Heat Transfer, Part B, vol. 34, pp. 191-213, 1998. Abstract-The Skew Central Difference Scheme is combined
with the Normalized Variable Formulation to yield a
new bounded Skew Central Difference Scheme. The newly
developed scheme is tested and compared with the Upwind
scheme, the bounded skew upwind scheme, and the high
resolution SMART scheme by solving four problems: (i)
pure convection of a step profile in an oblique velocity
field; (ii) sudden expansion of an oblique flow field
in a rectangular cavity; (iii) driven flow in a skew
cavity; (iv) gradual expansion in an axi-symmetric
non-orthogonal channel. Results generated reveal the
new scheme to be bounded and to be the most accurate
among those investigated. Abstract- A number of High-Resolution (HR) schemes
are reformulated in streamline-based coordinates and
bounded using the Convection Boundedness Criterion
(CBC) in the context of the Normalized Variable and
Space Formulation methodology (NVSF). This new approach
yields a family of Very High-Resolution (VHR) schemes
that combines the advantages of the traditional HR
schemes with the multi-dimensional nature of streamline-based
schemes. The resultant VHR schemes, which are based
on the MINMOD, OSHER, MUSCL, CLAM, SMART, STOIC, EXPONENTIAL,
and SUPER-C HR schemes, are tested and compared with
their base HR schemes by solving four problems: (i)
pure convection of a step profile in an oblique velocity
field; (ii) sudden expansion of an oblique velocity
field in a rectangular cavity (iii) driven flow in
a skew cavity; (iv) and gradual expansion in an axi-symmetric
non-orthogonal channel. Results reveal that the new
schemes are bounded and are by far more accurate than
the original HR schemes in situations when the flow
is highly skew to the grid lines.
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| Conference Papers |
Comparison of Supersonic Droplet Mixing And Evaporation Between The Multiphase, MUSIG And H-MUSIG Models(PDF) 6th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries SINTEF/NTNU, Trondheim NORWAY 10-12 June 2008. Abstract-The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H-MUSIG) for the simulation of mixing and evaporation of droplets injected into a stream flowing at supersonic speeds. All algorithms, implemented within a finite volume method, use an Eulerian pressure-based formulation but differ in the representation of the disperse phase. In the full multiphase approach each droplet size is considered a phase with a phasic velocity, energy, and volume fraction equation. In the MUSIG model, there is only one disperse phase that is decomposed into N size groups, all moving at the same speed. To account for each size group, a size fraction equation is solved. The H-MUSIG model can be viewed as a blend between the full multi-phase approach and the two-phase MUSIG approach by subdividing droplets into classes with droplet size groups in each class sharing the same velocity. Turbulence in the gas phase is accounted for by using the k-ε two-equation model while an algebraic model is used for the disperse phase. Results in an axisymmetric geometry indicate that solutions obtained by the various techniques exhibit similar behaviour with differences in values being relatively small. A Coupled Finite Volume Solver for Incompressible Flows (PDF) Abstract-This paper reports on a pressure-based coupled algorithm for the solution of laminar incompressible flow problems. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a way similar to a segregated SIMPLE algorithm with the extended set of equations solved simultaneously and having diagonally dominant coefficients. The superiority of the coupled approach over the segregated approach is demonstrated by solving the liddriven flow in a square cavity problem using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled solver is grid independent. Moreover, recorded CPU time values reveal that the coupled approach substantially reduces the computational cost with the reduction rate for the problem solved increasing as the grid size increases and reaching a value as high as 115. Supersonic Turbulent Fuel-Air Mixing and Evaporation (PDF) Proceedings of the Twelfth IASTED International Conference on Applied Simulation and Modelling, Sept. 3-5, Marbella, Spain, pp. 1-6, 2003. Abstract-Supersonic mixing and evaporation of poly-disperse sprays in complex flow systems are important in many engineering applications. The Eulerian and Lagrangian methods are two essentially different approaches for modeling such two-phase flows. Considering sprays consisting of droplets of various diameters, the Lagrangian approach accounts for each droplet discretely, while the Eulerian approach model the droplets, through an averaging process, as a continuum representing a second phase in addition to the gas phase. In this paper, adopting the Eulerian approach, an all speed control volume-based numerical procedure for predicting turbulent mixing and evaporation of droplets of variable diameters is formulated and implemented. A Unified Formualation
for Geometric Conservation Based Multifluid Algorithms (PDF) Abstract- Over the past two decades important advances have taken place in CFD centered around increasing numerical accuracy through the development of high-resolution schemes and improving efficiency through devising better solution algorithms, better solvers, and increasing use of multigrid techniques. For the solution of single-fluid flow, a number of segregated solution algorithms have been developed such as the well-known SIMPLE [1], the PISO[2], and the SIMPLEX [3] algorithms, to cite a few. Additionally, several techniques to improve the performance, facilitate the implementation, and extend the capability of these algorithms have been advertised [4]. On the other hand, developments in segregated multi-fluid solution algorithms have not been as fortunate due to both the higher computational cost involved and the numerical difficulties that had to be first addressed in the simulation of single-fluid flow. Despite these difficulties, the SIMPLE approach has been extended to multi-fluid flow simulations through the development of the Inter-Phase Slip Algorithm (IPSA) and its variants by the Spalding Group at Imperial College [5,6,7] and the Implicit Multi-Field [8] algorithms (IMF) by the Los Alamos Scientific Laboratory (LASL) group [9,10,11,12,13]. However, in contrast with the widespread information available on single-fluid solution algorithms, much less information is available on multi-fluid solution algorithms, a fact that has confined their implementation to a small community, slowed their development, and isolated them from the newer developments in single-fluid flow algorithms. Darwish et.al. [14] showed that all segregated single-fluid pressure-based algorithms can be extended to multi-fluid flow simulations. This extension can be accomplished in two different ways depending on the constraint equation used in deriving the pressure correction equation. The Mass Conservation Based Algorithms (MCBA) and the Geometric Conservation Based Algorithms (GCBA) denoted the resulting two families. Having introduced the MCBA in a previous article[ Error! Bookmark not defined.], this paper presents the GCBA family, in which, the pressure correction equation is derived using, as a constraint, the overall volume conservation equation. The new GCBA based algorithm that accounts implicitly for the volume fraction-pressure-velocity coupling is also introduced. The formulation is done using a unified, compact, and easy to understand notation that can be expanded systematically to yield the coefficients of the pressure correction equation. Results for compressible and incompressible test problems are also presented. An Exact r-Factor
TVD Formulation For Unstructured Grids (PDF) Abstract-The implementation of TVD schemes within a multi-dimensional structured grid environment is rather well understood. With the increasing importance of unstructured grid for CFD applications, a number of approaches have evolved for the implementation of these schemes within an unstructured grid finite volume method framework. Unfortunately none of these approaches has been comprehensive enough to permit the general implementation of TVD–based schemes in unstructured grids, and/or accurate enough to recover the exact TVD formulation in structured grids. In this paper we propose a simple method that allows the implementation of the full spectrum of TVD schemes in unstructured grids, while recovering their exact formulation on structured grids. Four schemes implemented using this approach, TVD-MINMOD, TVD-MUSCL, TVD-SUPERBEE, TVD-OSHER, are tested and compared to Bruner’s TVD formulation [1], and to the Barth and Jesperson linear reconstruction scheme [2] by solving two problems involving advection of a step and a sinusoidal profile. Results indicate that the Bruner formulation yields, for the same original TVD scheme, overly diffusive results when compared to the current method. The BJ-MUSCL and TVD-MUSCL are shown to be comparable and more accurate than the OSHER scheme. The SUPERBEE performs best though showing tendency for stepping the modeled profile. In all tests the current method is found to retain the behavior of the structured grid TVD formulation. On the Performance
of Mass Conservation Based Algorithms for Multi-Phase flows (PDF) Abstract- This work is concerned with the implementation and testing, of four incompressible-segregated multi-phase flow algorithms that belong to the Mass Conservation Based Algorithms (MCBA) group in which the pressure correction equation is derived from overall mass conservation. The pressure correction schemes in these algorithms are based on SIMPLE, SIMPLEX, PISO, and PRIME. Solving two one-dimensional two-phase flow problems spanning the spectrum from bubbly to gas-solid flows assesses the performance and accuracy of the multi-phase algorithms. The main outcome of this study is a clear demonstration of the capability of all MCBA algorithms to deal with multi-phase flow situations. Moreover, results displayed in terms of convergence history plots and CPU-times, indicate that the performances of the MCBA versions of SIMPLE and SIMPLEX are very close. As expected, the PRIME algorithm is found to be the most expensive due to its explicit treatment of the phasic momentum equations. The PISO algorithm is generally more expensive than SIMPLE and its performance depends on the type of flow and solution method used. A Finite-Volume
Algorithm for all Speed Flows (PDF) Abstract- A new collocated finite volume-based solution procedure for predicting viscous compressible and incompressible flows is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regimes. Pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density which become very small at low Mach numbers. The newly developed algorithm has two new features; (i) the use of the Normalized Variable and Space Formulation methodology to bound the convective fluxes; and (ii) the use of a High-Resolution scheme in calculating interface density values to enhance the shock capturing property of the algorithm.
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| Reports |
Development and Testing of a Robust
Free-Surface
Finite Volume Method (PDF) Summary- A
robust numerical technique for the simulation of
Free-Surface Flows was developed, implemented and
tested. The technique is based on the Finite Volume
method, uses unstructured grids for better geometric
flexibility, a pressure-based multi-fluid algorithm and
a high order discretization in both the spatial and time
domains. The accuracy of the method was deemed to be an
essential feature, to this end in the spatial domain
state-of-the-art high resolution (HR) advection schemes
are used in addition to a family of fifth order accurate
very High resolutions (VHR) schemes. In the time domain,
in addition to the standard Crank-Nicholson scheme, two
new discretization schemes were developed: a compressive
transient scheme and a second order bounded transient
scheme based on the second order backward Euler scheme.
A series of test were used to validate the accuracy and
robustness of the code. Result indicate that use of the
widely popular first order accurate schemes whether in
the transient (First order Euler scheme) or spatial
(UPWIND scheme) domains is not an option in free-surface
simulation as it leads to substantial unphysical
distortion in the simulated free surface. The
Crank-Nicholson and SMART schemes were found to be a
good combination for the transient and spatial domain
discretizations, with respect to accuracy and
robustness. Robustness was tested on a very tough dam
break simulation involving a returning wave, and results
were very satisfactory.
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