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- Turbulence models for CFD in the 21st century; Example 6

two jets are supposed to be confined within an outer cylindrical pipe in which the axial velocity and effective viscosity are as indicated here and here The flow is from left to right and the radial dimension has been increased ten fold The concentration dimension is divided uniformly into 50 equal intervals so a 50 fluid model is in question Click below for some animated fluid concentration contours first for CONMIX 1 0 and then for CONMIX 10 0 Fluid 50 the suddenly injected reactant Fluid 1 the other reactant Fluid 32 with a high concentration of injected material Fluid 16 with a moderate concentration of injected material Fluid 8 with a lesser concentration of injected material Fluid 4 with a still smaller concentration of injected material Fluid 2 with a very low concentration of injected material Suppose that fluid 32 is the one which produces the most colour Then compare its concentration contours at the 20th time step for the two CONMIX values The maximum values in the first case is 1 E6 times that of the second It is evident that the effect of a ten fold change in CONMIX is profound therefore it should easily be possible

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/turb2000/examp006.htm (2016-02-15)

Open archived version from archive - Turbulence models for CFD in the 21st century; Example 7

21st century by Brian Spalding of CHAM Ltd October 2000 Invited lecture presented at ACFD 2000 Beijing Example 7 Link to a lecture in the PHOENICS On Line Information System

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/turb2000/examp007.htm (2016-02-15)

Open archived version from archive - PHOENICS Online

As an alternative or supplement to standard licensing terms PHOENICS is accessible on line Unlimited interactive access is provided on a month by month basis ideal for users wishing to make infrequent or project based use of the code or

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_info/p-online.htm (2016-02-15)

Open archived version from archive - Multi-fluid Combustion Model

proportion of each box represent the mass fraction A 2D population e PDAs and CVAs Three and four D populations can be envisaged but they are harder to draw Material attributes which are not discretised ie not selected to be PDAs are called continuously varying attributes CVAs CVAs are treated as uniform in value but different from each other within each component of the population and in each element of space time PDAs are treated as uniform in value but different from each other only within each element of space time The distinction between the two kinds of attribute is arbitrary the analyst chooses as PDAs the attributes of which the fluctuation are most likely to be physically significant for example the density when gravitation influences the flow f What is meant by multi fluid Each component of a population is regarded as being a distinct fluid MFM models are called 2 fluid 4 fluid 100 fluid etc according to the number of distinct fluids which are in use If the selected PDA for a steam water mixture is density and only two value bands are chosen with the dividing value equal to the arithmetic mean density of steam and water the population is one dimensional with two components It could be called a 2 fluid model and indeed the IPSA 2 phase flow model which has been in use for nearly two decades is of this kind An implication is that the steam and water temperatures which are CVAs have each only one value at a given point in the flow If it were then decided also to take account of the fluctuations of temperature dividing the whole range into 10 equal intervals temperature would have become the second PDA The population would be 2 dimensional and a 20 fluid model would have resulted g What governs the mass fractions of distinct fluids The task of numerical simulation of turbulence with or without boiling condensation combustion etc thus becomes that of computing values of the mass fractions of the distinct fluids MFDFs together with their associated continuously varying attributes CVAs at all locations and times within the domain of interest The said values are influenced by the physical processes of convection diffusion laminar and turbulent and sources These and their interaction through the conservation laws of physics are expressible by way of differential equations of well known forms and properties h Solving the equations So well known are the equations that many widely available computer programs are equipped to solve them One such is the PHOENICS Shareware package If as usual they are of the finite volume kind the programs compute the MFDFs and associated CVAs by solving a large number of inter linked and non linear balance equations by iterative techniques The most time and attention consuming part of the modelling exercise is then the formulation of the source and sink terms which express chiefly how the distinct fluids interact with each other In the work to be

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/mfm/mfm4.htm (2016-02-15)

Open archived version from archive - phoeintr.htm

Editor The appearance of VR Editor the screen is shown on the next panel The image comes from one of the examples in TR 324 Starting with PHOENICS VR However no attempt will be made to describe it in detail because the information is best conveyed by way of a live demonstration or hands on use of the code It suffices therefore to say here that objects of all kinds blockages inlets outlets sources etc can be brought in by appropriate mouse clicks and then given such locations shapes sizes materials and other attributes as are needed to start the flow simulating calculation This is the top part of the menu which appears when the Main Menu button is pressed It enables whole domain settings to be made What the Virtual Reality Editor creates The VR Editor records the settings made by the user during his editing session in an ASCII file known as Q1 This file can be read understood if the user knows something of PIL the PHOENICS Input Language and edited Usually however it will simply be stored for later use In any case the flow simulation can begin immediately if the user wishes because two other files will also have been automatically written one of which FACETDAT conveys the necessary geometrical information while the other EARDAT carries everything else that the solver module needs to know The switching from the VR Editor to the solver and for that matter to any other PHOENICS module is rendered particularly easy by the pull down menus accessible from the top bar of the VR Editor screen EARTH The solver EARTH starts with a MAIN program open to users for re dimensioning operations The other user accessible source subroutines are GROUND GREXn i e GROUND example number n and others of the same kind EARTH contains sequences for storage allocation formulation of finite volume equations iterative solution of finite volume equations calling GROUND when required termination of iteration sequences output of results A Typical EARTH Convergence Monitor Plot GROUND GROUND is a subroutine which is called by EARTH at pre set points of the solution cycle If the user inserts appropriate FORTRAN statements at the entry points in GROUND EARTH absorbs these into the solution process Special communication subroutines allow the user to extract information from EARTH manipulate it in GROUND and then return new information or instructions to EARTH Many service sub routines are attached performing commonly needed arithmetic operations These greatly reduce the user s need to write FORTRAN coding sequences Built In Features Of EARTH Conservation principles PHOENICS sets up and solves finite domain equivalents of the basic differential equations It thus embodies the laws of conservation of mass momentum and energy for either one or two phases More than 2 phase flows can also be represented in a number of ways Any property obeying a balance equation can be represented including species concentration turbulence energy vorticity and its fluctuations radiation fluxes electric potential etc Solution procedures PHOENICS contains solvers for sets of linear simultaneous equations Options include point by point slab wise and whole 3D field The coupled hydrodynamic equations are solved by the so called SIMPLEST procedure For two phase flows the IPSA version of this is used Details of these procedures are given in the published CFD literature Handling special requirements EARTH can handle problems which are steady or unsteady parabolic or elliptic and 0D 1D 2D or 3D EARTH accepts grid definition material property initial value and boundary condition information transmitted from the satellite EARTH turns to GROUND or GREXn etc for further data settings when so instructed EARTH arranges for print out of required output and also of warnings diagnostics etc What is not built in Turbulence model chemical kinetic interphase transport radiation flux and other coding sequences are attached through GROUND to the outside of EARTH They can therefore be inspected modified or replaced by the PHOENICS user The built in solvers can also be inspected modified and replaced should the user desire EARTH is thus a glass box not a black box Display via VR The Virtual Reality Interface of PHOENICS can also operate as a results display device It is then called the VR Viewer An example VR Viewer plot is shown in the next image once again taken from an example in TR 324 Starting with PHOENICS VR A Typical VR Viewer Plot The main advantage of VR Viewer over the older PHOTON program is the ease with which it enables users to view streamlines vectors iso surfaces and contour plots PHOTON A further menu driven interactive program called PHOTON can create from PHOENICS output grids and grid outlines contour plots in either colored line or filled area modes streamlines in any color vector plots for either of the two phases surface plots magnified views of parts of the field arbitrarily chosen view points in multiple windows A Typical PHOTON Plot AUTOPLOT AUTOPLOT is the third member of the PHOENICS graphics family It is a command driven which can plot x y graphs from any combination of PHOENICS output files and user supplied data files This allows for easy comparison of PHOENICS solutions with experimental or analytical data manipulate the data in a number of ways such as adding or subtracting constants multiplying or dividing by constants raising to powers taking logs and antilogs and many more The data can be presented in a number of line styles A Typical AUTOPLOT Picture Other Input and Output Facilities Many more input and output features of PHOENICS can be operated from the satellite Users for whom the built in facilities do not suffice may introduce their own input output sequences via the FORTRAN of SATLIT and GROUND GROUND located sequences for problem specific input output source terms boundary conditions or physical properties are switched on by setting special flags in the satellite An exemplary GROUND subroutine GREXn contains many frequently used settings When these do not suffice the task of

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/general/phoeintr.htm (2016-02-15)

Open archived version from archive - THE MATHEMATICAL BASIS OF PHOENICS

It is not necessary to march through time to reach the steady state Transient Problems PHOENICS can cope with constant and variable time steps The time step size can be a function of time 4 Grids Storage locations Vector quantities are computed by reference to cells which are staggered with respect to the scalar cells 3 velocities and 1 scalar share the same cell index IX IY IZ Any scalar or vector quantity can only be referenced by a unique IX IY IZ index Thus the velocity on the West face of the cell P above belongs to the West scalar cell Types of Grid PHOENICS grids are structured cells are topologically Cartesian brick elements PHOENICS grids may be Cartesian Cylindrical polar Body fitted orthogonal or non orthogonal In all cases the grid distribution can be non uniform in all coordinate directions For cylindrical polar coordinates the following orientation is used X or I is always the angular direction Y or J is always the radial direction Z or K is always the axial direction 5 The Balance Equation Basic form The basic balance or conservation equation is just Outflow from cell Inflow into cell net source within cell The quantities being balanced are the dependent variables from the earlier panel mass of a phase mass of a chemical species energy momentum turbulence quantities electric charge etc Terms The terms appearing in the balance equation are Convection i e directed mass flow Diffusion i e random motion of electrons molecules or larger structures e g eddies Time variation i e directed motion from past to present accumulation within a cell Sources e g pressure gradient or body force for momentum chemical reaction for energy or chemical species The Generalized Form The single phase conservation equation solved by PHOENICS can be written as where f the variable in question r density vector velocity the diffusive exchange coefficient for f the source term Particular Forms Particular examples are Momentum Enthalpy Continuity where are the turbulent and laminar viscosities and Pr t Pr l are the turbulent and laminar Prandtl Schmidt Numbers Numerical solution The balance equations cannot be solved numerically in differential form Hence PHOENICS solves a finite volume formulation of the balance equation The FVE s are obtained by integrating the differential equation over the cell volume Interpolation assumptions are required to obtain scalar values at cell faces and vector quantities at cell centers No Taylor series expansion or variational principle is used Finite Volume Form After integration the FVE has the form where by continuity The neighbour links the a s have the form convection diffusion transient Correction Form The equation is cast into correction form before solution In correction form the sources are replaced by the errors in the real equation and the coefficients may be only approximate The corrections tend to zero as convergence is approached reducing the possibility of round off errors affecting the solution The neighbor links Increase with inflow velocity cell area fluid density and

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/general/maths.htm (2016-02-15)

Open archived version from archive - BOUNDARY CONDITIONS IN PHOENICS

stationary and moving walls in case 921 are specified as shown Moving wall at South side of domain at 1 deg WALL MOVING SOUTH 1 NX 1 1 1 1 1 1 COVAL MOVING U1 1 0 WALLVEL COVAL MOVING TEM1 1 0 1 0 Stationary wall at North side at 0 deg WALL NORTHW NORTH 1 NX NY NY 1 1 1 1 COVAL NORTHW U1 1 0 0 0 COVAL NORTHW TEM1 1 0 0 0 Stationary wall at West side at 0 deg WALL WESTW WEST 1 1 1 NY 1 1 1 1 COVAL WESTW V1 1 0 0 0 COVAL WESTW TEM1 1 0 0 0 Stationary wall at East side at 0 deg WALL EASTW EAST NX NX 1 NY 1 1 1 1 COVAL EASTW V1 1 0 0 0 COVAL EASTW TEM1 1 0 0 0 Note that the coefficients have all been set to 1 0 and the values to the wall surface values This suffices for laminar wall conditions Turbulent Wall Boundary Condition In a turbulent flow the near wall grid node normally has to be in the fully turbulent region otherwise the assumptions in the turbulence model are invalid The wall shear stress and heat transfer can no longer be obtained from the simple linear laminar relationships Unless a low Reynolds number extension of the turbulence model is used the normal practice is to bridge the laminar sub layer with wall functions These use empirical formulae for the shear stress and heat transfer coefficients Three types of wall function are available selected by the COVAL settings Coefficient GRND1 for Blasius power law Coefficient GRND2 for equilibrium Logarithmic wall function Coefficient GRND3 for Generalised non equilibrium wall function Coefficient GRND5 for Fully rough equilibrium Logarithmic wall function Example From The Library Library case 172 concerns the prediction of developing flow in a duct The k epsilon turbulence model is used The duct surface at the north side of the duct is represented as GROUP 13 Boundary conditions and special sources North Wall Boundary WALL WFUN NORTH 1 1 NY NY 1 NZ 1 1 COVAL WFUN TEMP GRND2 TWALL Note the use of the WALL command to locate the wall and activate wall friction effects The surface temperature is supplied via the COVAL for TEM1 The GRND2 in the coefficient slot activates logarithmic wall functions Inflow Boundary Condition All mass flow boundary conditions are introduced as linearized sources in the continuity equation with pressure P1 as the variable A mass source is thus where Cm and Vm are coefficient and value for P1 At an inflow boundary the mass flow is fixed irrespective of the internal pressure This effect is achieved by setting Cm to FIXFLU and Vm to the required mass flow The sign convention is that inflows are ve outflows are ve A fixed outflow rate can thus be fixed by setting a negative mass flow Example From The Library Library case 274 concerns the flow over a simplified van geometry The inflow boundary at the low end of the solution domain is represented as GROUP 13 Boundary conditions and special sources Upstream boundary INLET UPSTR LOW 1 NREGX 1 NREGY 1 1 1 1 VALUE UPSTR P1 14 0 VALUE UPSTR W1 14 Note that for an INLET the VALUE command for P1 sets the mass flux This is often set as RHOIN VELIN the inlet density inlet velocity The mass flux is fixed and the in cell pressure is allowed to float The VALUE command for W1 sets the velocity of the inflowing stream In this case all other variables are taken to be 0 0 at the inlet If they are not then VALUE commands would have to be added Fixed Pressure Boundary Condition This is the case of a mass flow boundary where the pressure is fixed irrespective of the mass flow As with any other variable the pressure is fixed by putting a large number for Cm and the required pressure for Vm For numerical reasons FIXVAL tends to be too big A Cm of about 1E3 usually suffices The Encyclopaedia gives further guidance The direction of flow is then determined for each cell in the PATCH by whether Pp Vm or Pp Vm The first produces local outflow the second local inflow Example From The Library The exit boundary in case 274 is a fixed pressure boundary set as Downstream boundary PATCH DWSTR HIGH 1 NREGX 1 NREGY NREGZ NREGZ 1 1 COVAL DWSTR P1 FIXP 0 COVAL DWSTR U1 ONLYMS 0 0 COVAL DWSTR V1 ONLYMS 0 0 COVAL DWSTR W1 ONLYMS 0 0 In this case the in cell pressure is fixed by the COVAL for P1 and the mass flux is adjusted to satisfy continuity The direction of flow is determined by whether the in cell pressure is or the fixed value The COVALs for U1 V1 and W1 are supplied in case part of the boundary should be an inflow they specify velocities to be brought in They are not used in cells where in cell pressure external General Source Terms PHOENICS makes no distinction between boundary conditions and source terms Both are represented in the by now familiar TC V phi form In the lecture so far we have made a distinction between the true source S f and the boundary source Sbc The true source represents the fundamental parts of an equation which are not covered by the convective diffusive or transient terms These are coded in EARTH and hence are called the built in sources Built in Sources Examples of these are The pressure gradient sources in the momentum equations The centrifugal and Coriolis sources in the momentum equations in cylindrical polar co ordinates The negative of the substantial derivative of pressure in the enthalpy equation The viscous dissipation of heat in the enthalpy equation The built in sources can be switched off for individual variables by setting N as the first argument of TERMS

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/general/bcond.htm (2016-02-15)

Open archived version from archive - SOLUTION TECHNIQUES

TDMA is used which does require iteration A conjugate gradient version is also available The maximum number of iterations within the solver at a slab for a particular variable is controlled by LITER INDVAR Iterations stop when the errors sum to less than RESREF INDVAR and average changes from iteration to iteration are less than ENDIT INDVAR Because of non linearities and because off slab values have been taken as known it is seldom worth obtaining precise solutions at a slab It is much more economical to sweep the domain many times Slabwise solution is always used for parabolic flows as the values on the low side are indeed known In these cases it is essential to obtain fully converged solutions at each slab as each slab is visited only once 2 3 Whole field In this method the cell values of f are all new all links are correctly included a P f P new a N f N new a S f S new a E f E new a W f W new a H f H new a L f L new a T f T sources The whole field solver operates by a further extension of the TDMA A conjugate gradient solver is also available activated by setting CSG3 CNGR These also require iteration Iterations are controlled by LITER RESREF and ENDIT as for the slab solver Whole field solution can be specified for all variables and the pressure correction equation via the SOLUTN command or the menu Whole field solution is always preferable when non linearities are slight e g for heat conduction or velocity potential or other potential equations Whole field solution is always recommended for the pressure correction equation as this transmits effects of flow boundary conditions and blockages rapidly throughout the domain 2 Convergence Acceleration Devices PHOENICS possesses several solution accelerating devices namely over relaxation slabwise block corrections in the X Y and Z directions multi grid corrections on blocks of user selectable size and location This is especially useful in multi material problems Coupled Equations The momentum and continuity equations are linked in that the momentum equations share the pressure and the velocities and pressure via the density in compressible flows enter the continuity equation There is no direct equation for the pressure The task of all CFD codes is to join the variable without an equation pressure to the equation without a variable continuity PHOENICS does this using a variant of the SIMPLE algorithm namely SIMPLEST SIMPLEShorTened Simplest The main steps in both the SIMPLE and SIMPLEST algorithms are Guess a pressure field Solve the momentum equations using this pressure field thus obtaining velocities which satisfy momentum but not necessarily continuity Construct continuity errors for each cell inflow outflow Solve a pressure correction equation The coefficients are area d vel d p and the sources are the continuity errors Adjust the pressure field correspondingly Adjust the velocity fields correspondingli i e as new velocity is old velocity d vel

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/numerics/solution.htm (2016-02-15)

Open archived version from archive

web-archive-uk.com, 2017-12-17