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- SPECIFIC HEATs at constant pressures, CP1 and CP2

equal to the specific heat times the absolute temperature This effective specific heat Cp eff is defined as the enthalpy of the material at the prevailing temperature minus the enthalpy of the same material when the temperature is zero on the currently used temperature scale Thus Cp eff H H 0 Tabs where h 0 is the temperature at absolute zero This differs from the conventional specific heat at constant pressure Cp which is defined as the rate of change of enthalpy with temperature but it has the same dimensions and is of the same order of magnitude The following diagram explains the relation between the quantities H enthalpy The curve represents the enthalpy versus temperature relationship T The line represents the tangent at the working point H T and has the slope Cp H 0 The line has the slope Cp eff used by PHOENICS 0 Tabs Absolute Temperature The following remarks may be helpful The reason for using Cp eff rather than Cp is computational and internal coding economy for the above equation makes if easy to deduce temperature from enthalpy or enthalpy from temperature The temperature which is deduced from enthalpy because the latter is the solved for quantity is conventionally given the name TMP1 or TMP2 according to phase The temperature which is solved for directly is conventionally given the name TEM1 or TEM2 according to phase Then the enthalpies are the derived quantities Temperature can be measured on any scale chosen by the user but the absolute temperature Kelvin scale and the Celsius scale the zero of which is 273 on the Kelvin scale are the most common The value of H 0 depends of course on which temperature scale is in use as does the value of Cp eff Cp eff and Cp are

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

Open archived version from archive - spell.htm

translated into understandable English The translation includes information about the grid the variables solved and or stored material properties patches solver options etc It is activated by typing LOAD 020 or 020 when the SATELLITE is running in TALK T

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

Open archived version from archive - subgrd.htm

values he wishes to ascribe to the indices and exponents in order to produce the required fineness and distribution of grid The syntax is SUBGRD DIR L1 L2 DIST POW This sets GRDPWR type grids over a portion of the grid DIR is the direction and may be X Y Z or T L1 and L2 are the first and last cells in the section of sub grid L1 must

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

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flux ii For laminar flow kf is simply the laminar thermal conductivity For turbulent flow kf is the turbulent thermal conductivity so that Gf is given by Gf St Ur cp r St is the Stanton number computed from the wall functions Ur is the absolute magnitude of the relative velocity parallel to the surface 12 The mean conductive heat flux The mean conductive heat flux is given by q s Gs Ti Ts 4 Ts is the adjacent solid temperature Gs is the mean solid side heat transfer coefficient in W m 2 K given by Gs ks ds ks is the thermal conductivity of the Solid ds is the normal distance from the surface to the first grid point in the adjacent solid 13 Determination of the surface temperature Substitution of equations 2 3 and 4 into the heat balance equation 1 gives the equation for the surface temperature of the thermal zone i viz Ti 4 sum Gri j Ti Gf Gs sum Gri j Tj 4 Gf Tf Gs Ts q 0 5 Ti is calculated iteratively from equation 5 by application of the Newton Raphson method 14 Activation Essential Q1 settings i The S2SR model is activated by setting S2SR T To activate the solution of the energy equation set SOLVE TEM1 If TEM1 is in Kelvin then TMP1A is 0 0 if TEM1 is in Celsius TMP1A should be set to 273 0 The solution of the TEM1 equation requires definition of material type via a type flag assigned through the storage of the PRPS variable To activate this store set STORE PRPS and initialise the PRPS field using FIINIT and or PATCH INIT commands 15 Activation Essential Q1 settings ii PATCH and COVAL commands are required to define the location and type of the boundary condition for each radiative thermal zone The PATCH command is used to locate thermal zones For radiative PATCHES the NAME must start with RI where RI indicates that the patch is a thermal zone participating in internal radiative heat transfer and is a three digit number representing the thermal zone number These numbers must be consecutive starting at 1 and the patches have to be defined consecutively in the Q1 file The TYPE must be an AREA i e NORTH SOUTH etc 16 Activation Essential Q1 settings iii The following restrictions apply in defining the LOCATION If the zone is a surface of a solid for which conjugate heat transfer is present then PATCH located on the solid side If the zone is a surface on the domain edge or on a completely blocked region i e conjugate heat is not present then PATCH located on the fluid side 17 Activation Essential Q1 settings iv COVAL Command If the surface temperature is to be obtained from the heat balance set CO and VAL to GRND1 For fixed heat flux boundary condition set CO to GRND1 and VAL to required heat flux For fixed temperature boundary condition set CO

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

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cp T H mf where cp is constant pressure specific heat T is absolute temperature H is heat of combustion and mf is mass fraction of unburned fuel The ratios of the masses of fuel oxidant and products engaging in a reaction are 1 r and 1 r respectively where r is a constant Typically r 3 5 when the fuel is a hydrocarbon and the oxidant is undiluted oxygen combustion 9 2 The simple chemically reacting system lecture SCRS 3 1 20 Equality of diffusion coefficient An often used extension of the SCRS definition is that the diffusion coefficients of fuel oxidant and product are all equal to each other and to the diffusivity of heat so their Prandtl Schmidt numbers are equal This is not far from the truth for laminar gaseous flow and it is very close to the truth for turbulent fluids An important consequence is that it is possible to describe the composition of a reacting mixture by just two variables for example mf and f where f is the mixture fraction ie the mass of material originating from fuel per unit mass of mixture regardless of whether it is burned or not combustion 10 2 The simple chemically reacting system lecture SCRS 4 1 20 Composition of fully reacted gas 1 x 0 1 combustion 11 2 The simple chemically reacting system lecture SCRS 5 1 20 Reaction rate for fixed f and h oxygen x x x x x x rate x x x x x 0 reactedness T Tu Tb Tu 1 combustion 12 2 The simple chemically reacting system lecture SCRS 6 1 20 Features relevant to PHOENICS The f and h equations have no source terms Temperature can be deduced from h via T h mf H cp mox can be deduced from mox A B f C mf where A B C are constants The mf equation has a reaction rate source of the form source of fuel const mf mox function of T When the reaction rate constant is large there is no need to solve for mf it depends only on f see panel 10 above combustion 13 2 The simple chemically reacting system lecture SCRS 7 1 20 How sources terms are calculated The equation source const mf can be created by PATCH any name VOLUME COVAL patch name FUEL const 0 0 for this makes source coeff 0 0 fuel The equation source const 1 rctd rctd expnt can be created by the following library case 109 A non linear source of RCTD is present PATCH CHSOTERM VOLUME 1 NX 1 1 1 1 1 LSTEP COVAL CHSOTERM RCTD GRND7 1 0 RSG3 1 0E8 RSG4 6 0 Patch names starting CHSO activate chemical sources combustion 14 2 The simple chemically reacting system lecture SCRS 8 1 20 How densities may be calculated Density is calculated as p mol wt gas const T via RHO1 GRND6 RHO1A WFU RHO1B WAIR RHO1C WPR which activates this

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

Open archived version from archive- FREE.HTM

is applicable to unsteady incompressible flows only in one two or three dimensions It can simulate convoluted and overturning surfaces Since the SEM employs a fully explicit formulation it is constrained by the Courant criterion for time step increment for the stability of the solution The SEM generally works well for highly non orthogonal grids with NONORT set to TRUE It can also cope with heat transfer between the fluids and with conjugate heat transfer between the fluids and surrounding and immersed solids See the entry on S E M Scalar Equation Method for instructions on how to activate it The HOL method determines the location of the interface from the solution of the liquid balance equations The HOL method is applicable to both steady and unsteady incompressible isothermal flows in one two or three dimensions It is restricted to flows that are not convoluted in interconnected blocked regions for example and exhibit no overturning of the interface The HOL method is fully implicit and therefore suffers no restrictions for unsteady cases on the time step increments The HOL method does not generate numerical diffusion which implies less emphasis on grid size constraints However for highly non orthogonal grids convergence problems may occur with the HOL method See the entry for H O L for instructions on how to activate it in PHOENICS FREE Surface Flows See the Encyclopaedia entry Free surface flows FREEE PIL real flag value 9 0 group 13 FREEE is a PATCH type used for setting sources per unit FREE East area by way of COVAL in group 13 Note that FREE here signifies the cell face area available for flow i e the geometrical area multiplied by the cell face porosity The types FREEE FREEN FREEH and FREEVL should be used only for cell faces

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

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per unit volume in x direction V W displacements in y and z directions C1 C2 C3 are functions of Young s modulus Poisson s ratio the x direction VELOCITY u obeys at low Reynolds number del 2 u d dx p c1 fx c2 0 where p pressure fx external force per unit volume in x direction c1 c2 1 viscosity Notes The equations are similar if p c1 D C1 Te C3 ie D p c1 Te C3 C1 and fx c2 Fx C2 The expressions for C1 C2 and C3 are C1 1 1 2 PR C2 2 1 PR YM where PR Poisson s Ratio C3 2 1 PR 1 2 PR YM Young s Modulus In Te the local temperature is measured above that of the unstressed solid in the zero displacement condition The linear relation between D ie d dx U p and Te can be effected by inclusion of a pressure and temperature dependent mass source term d Deduction of the associated stresses and strains The strains ie extensions ex ey end ez are obtained from differentiation of the computed displacements Thus ex d dx u ey d dx v ez d dx w Then the corresponding normal stresses sx sy sz and shear stresses tauxy tauyz tauzx are obtained from the strains by way of equations such as sx YM 1 PR 2 ex PR ey tauxy YM 1 PR 2 0 5 1 PR gamxy where gamxy d dy u d dx v The relevant computer coding in PHOENICS is to be found in the open source Fortran sub routine GXSTRA F e The SIMPLE algorithm for the computation of displacements PHOENICS employs a variant of the SIMPLE algorithm of Patankar Spalding 1972 for computing velocities from pressures under a mass conservation constraint In this algorithm p is computed from D above with u not U the f p D function being linear in simple circumstances Therefore a CFD code based on SIMPLE can be made to solve the displacement equations by eliminating the convection terms ie setting Re low and making D linearly dependent on p and temperature T The modular structure of PHOENICS has made this rather easy to do The staggered grid used as the default in PHOENICS proves to be extremely convenient for solid displacement analysis the u v and in 3D w are stored at exactly the right places in relation to P f A simple example of flow influenced stress The following sketch illustrates a combined mechanical and thermal stress situation in which the fluid flow plays a part The task is to compute displacements and thence strains and stresses in the heated block load V V g The computational problem The independent variables are y z the flow is steady and the body is axi symmetrical so neither time nor circumferential coordinate x has an influence The dependent variables are v w velocities or displacements P pressure or dilatation T temperature Derived variables Te

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

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developed to match practitioners requirements whilst consistently using plain English The menus are accessed by a branch type structure and all defaulted values are set to describe a realistic tower size and condition which you can modify to your own requirements Options can be chosen by mouse or keyboard and a graphical capability enables the visualisation of the tower during set up phase Flow Visualisation To post process results TACT can use one or the other of the two stand alone packages from the PHOENICS computational suite AUTOPLOT is the graph plotting package This program enables you to trace profiles of wind pressure velocity temperature water vapour concentration and all other results derived from TACT It can also be used to plot results from multiple TACT runs in order to display trends from parameric studies PHOTON is the visualisation package which enables you to view wind vectors and contours of properties in colour thus enhancing the presentation of results for clear and concise interpretation Picture Tower performance as a function of wind speed for various water distributions Picture Vapour contours plotted through the centre plane of a cooling tower Picture Wind vectors plotted on a horizontal lane at basin level TACT Menu Display TACT Thermal Analysis of Cooling Towers TACT can be used to optimise the design of new cooling towers by way of parametric studies and performance improvements of existing ones from changes in fill design or water distribution can be tested Results provided by TACT predictions can include performance related data such as 1 Air temperature distribution and water vapour concentrations in and around the tower 1 Water temperatures within the tower N Outlet water temperature N Evaporative water losses N Air flowrate through the tower N Thermal performance of the tower as a whole On the other hand Most contemporary models are too simplistic for reliable predictions of cooling tower performance mainly due to their reliance on one or two dimensional representation of the geometry Anything less than a three dimensional model will not account correctly for local wind patterns that can have a profound effect on cooling rates Before TACT there was no rigorous three dimensional model Many existing models are based on expiricisms derived from measured data These seldom hold true for other cooling towers of different size and capacity or that operate in a different environment Main features of TACT Ease of use TACT has a user friendly menu which provides a straightforward and concise method for data input No specialist computer or mathematical knowledge is required Geometric Features TACT provides a full three dimensional representation of the cooling tower The menu permits the user who may be a designer or operator to prescribe and modify details of the tower layout such as location and characteristics of the air inlet fill zone eliminator sprinklers struts supports and rain zone which can all be studied in detail Mesh Generator TACT works by solving balance equations for conservation of mass momentum and energy across discrete multiply

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

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