A New Approach to Open CFD Authors: Colinda Francke, Yingchen Li, Kilian Claramunt, Charles Hirsch NUMECA International, Chaussée de la Hulpe, 187-189, 1170, Brussels, Belgium Abstract The main components of an Open CFD concept can be considered as: access to all functionalities and modules of a basic CFD code; total flexibility in modifying or adding new physical models and boundary conditions; ability to share modifications to the basic code among a wide community of users, including distance collaboration; straightforward access for large scale simulations. NUMECA has developed the OpenLabs environment to respond to these requirements, offering a new approach to Open CFD. OpenLabs is a highly user-friendly mode of operations, conceived as a dialog system with the basic CFD code. It provides access to routines of the basic CFD code, to the variables of the routines and to all existing physical models and properties. In a few lines of text, transport equations, source terms, initial or boundary conditions, fluid properties, algebraic relations, thermal and transport properties are modified or added. As this text is easy to understand and does not require any knowledge of programming or code structure, it can be used by anyone in the CFD community as a starting point for new models. The created Labs can remain proprietary or freely available, through an OpenLabs community, established in order to share Labs applications. The underlying code FINE /Open is a highly robust unstructured solver with a variety of models like a.o. turbulence, multiphase, combustion, radiation, providing altogether a highly professional quality assured CFD background. It covers a wide range of applications, from incompressible to supersonic and hypersonic, from perfect gas to liquids and condensable fluids, internal and external flows, fixed or rotating frames of reference. The paper provides a description of the OpenLabs structure and mode of operation, illustrated by a few examples, including the introduction of an actuator disk model for rotating components and solving an electric potential field near a plasma actuator. 1
1. Introduction The main components of an Open CFD concept can be considered as follows: access to all functionalities and modules of a basic CFD code; total flexibility in modifying or adding new physical models, involving a large range applications; ability to share the modifications to the basic code among a wide community of users, including distance collaboration; straightforward access for large scale simulations. NUMECA has developed the OpenLabs environment to respond to these requirements, offering a new approach to Open CFD as put forward in this paper. The OpenLabs environment and its underlying code FINE /Open are described and examples of applications benefiting from such approach are given in the next sections. 2. Description of OpenLabs OpenLabs is a highly user-friendly mode of operations, conceived as a dialog system with the basic CFD code. It provides access to routines of the basic CFD code, to the variables of the routines and to all existing physical models and properties, and therefore the ability to customize the physical models. 2.1 Principle of OpenLabs The general principle of OpenLabs is to plug the users physical models and parameters without programming efforts to a highly modular CFD solver through dynamic libraries. A large range of the physical models of the basic CFD solver can be accessed, including the turbulence models, wall functions, equation of state, transport properties, combustion, radiation, etc. The user only needs to write the physical models in text (here and after referred to as a Lab) using an intuitive meta-language as if writing a technical paper. Then OpenLabs will take care of the rest to prepare automatically the dynamic library, i.e. discretization, applying suitable numerical techniques, invoking implicit/explicit solver, etc. In addition to the easy text format, OpenLabs shows its user-friendliness through the possibility to simply copy/paste information from the basic solver into the Lab. An Analysis-button is available for this purpose. Performing such analysis with a simple click will show the available models and variables of the basic solver adapted to the project definition in the same text format of Labs. The result of the analysis can be copied and pasted into the Lab. Figure 1 gives the illustration showing how OpenLabs works. A CFD project is set-up based on the basic solver. With one mouse-click OpenLabs analyses the available models and variables from the basic solver and the CFD project and provides this information in Labs text format. This information can then be used in the Labs through 2
copy-paste. The individual user may create Labs from scratch or use already existing ones coming from the worldwide CFD community and/or Labs of physical models of the basic solver and combine them to fully customize the CFD models to the project at hand. Basic Solver Basic models CFD project OpenLabs Analysis Available models and variables Lab(s) Model processor C++ file & shared library Output Figure 1 Principle of OpenLabs 2.2 Functionalities in OpenLabs The physical models can be described in a modular way. OpenLabs provides various functionalities as building blocks for the Labs, which cover a large range of CFD applications. The functionalities include, Convection-diffusion-source transport equations and their associated objects, including diffusion coefficients, source terms, initializations and boundary conditions. The user can add an unlimited number of new transport equations, and can modify the existing ones from the basic solver. The convection-diffusion-source equations will be discretized using finite volume method with the user-specified scheme and resolved by a multi-step Runge-Kutta solver. For the source term, the point-implicit technique is available to improve the robustness. For the boundary condition, the Dirichlet, Neumann and Robin type are all available. Poisson equations: an implicit Gauss-Seidel solver can be used to solve the Poisson equations with alternate sweeping and successive over-relaxation. Equation of state: the basic solver has involved various fluid types, including incompressible fluid, perfect gas, real gas and condensable fluid. The equation of state selected from the basic solver can be partially or fully replaced with a set of relations. 3
Transport properties: the user can modify the laws of existing transport properties, e.g. viscosity, conductivity, and can define new transport properties. The laws of the wall, e.g. turbulence wall functions. The user can define the relation of the independent CFD variable between the wall and the adjacent inner nodes. The existing turbulence wall functions from the basic solver can also be modified. Algebraic relations and global quantities over geometries. The user can define the dependent CFD variables through algebraic relations. The global quantities like mass flow, the over-all loss, drag and etc. can be defined and given as an output. These dependent CFD variables/parameters can be visualized in the post-processor. With these functionalities, various applications have been implemented through OpenLabs, including turbulence and transition models, combustion models, radiation models, pollution models, complex state law of the fluid, active flow control, an atmospheric boundary layer model and etc.. Prospectively, OpenLabs provides the possibility to have un-limited applications (cost functions) of using the adjoint method. The functionalities are still increasing, for example: Convection velocity. The user can define various convection velocities, which can be used to develop the Euler-Euler multiphase model. In adjoint methods, it can be used to define the convection term of the adjoint transport equation of a scalar, which has the inverse velocity of the flow. Local linear system. For example, the boundary conditions of several variables can be imposed implicitly through a linear system. Shell convective-diffusion-source equation. Like shell conduction, the convection and diffusion of a scalar are limited on the surfaces in some physical models, for example, the icing model. 2.3 Methodology OpenLabs relies on C++ language. However, the user doesn t need to know C++ programming as OpenLabs packages the processes of solving CFD problems in several functionalities, as mentioned above and provides various prototyped numerical techniques, for example, convection discretization using the first order and high order upwind scheme, discretization of diffusion, the poin-implicit technique for the source terms, the laws of the wall, etc. In addition, OpenLabs provides the possibility to use various mathematical tools like for example, CST/Linear interpolation, a Newton-Raphson implicit solver, Leastsquare/Green-Gauss gradient, tabulation of analytical expressions and trapezoidal integration. All these functionalities are well packaged and the user doesn t need to care about the discretization, the numerical techniques, the memory allocation and all the programming details. The functionalities can be applied through a few lines of text. For example, to add a convection-diffusion-source transport equation, the following lines of text can be used: =>EQUATIONS @PDE: phieq ->EXPRESSION: DDT(phi)+CONV(phi)=DIFF(coefficient)+SOURCE(source) 4
->UseCustomBC: BC1, ALLINLETS ->UseCustomBC: BC2, ALLSOLIDS ->InitializeTo: phifield The diffusion coefficient and source term used in the PDE expression should be defined respectively, =>ALGEBRAIC_DIFFUSION_COEFFICIENTS @ALGDIFFCOEFF: coefficient ->EXPRESSION: <expression of coefficient> =>SOURCETERMS @SOURCE: source ->EXPRESSION: <expression of source> Behind this, OpenLabs will allocate the memory for the new variable phi, discretize the spatial terms, compute the residuals, and invoke the multi-step Runge-Kutta solver. Another example is to solve an implicit expression: the following lines can be used to solve U from the equation: U t U 1 yu ln( k ) b 0, 1 ->EXPRESSION: SOLVE(UTau){ Zero_Function: 1/k*log(distanceToWall*UTau/nu) + b0 Ut/UTau } Behind this command, the variable UTau will be solved by a Newton-Raphson solver, where the Jacobian of the function is computed numerically. To improve the robustness of solving UTau, the user may wish to impose the analytical Jacobian and clip: Jacobian: 1/k/UTau + Ut/UTau/UTau LowerLimit: 1e-10 More advanced options are available that can be tuned by the user, for example: ->Convective_Scheme: UpwindFirstOrderConservative is the default setting in the definition of a PDE, however it can be modified by: ->Convective_Scheme: UpwindHighOrderConservative The commands are also accompanied with error handling. For example, the BC1 used in the earlier example of the PDE phieq has to be defined. If there is no command to define BC1, an error will be reported before the library is generated. The error handling ensures the whole definition as written in the Lab is complete and consistent. In addition, the user may start from an empty template to create a new Lab or use an already existing Lab as a template. To prepare a Lab the user also has access to the variables to formulate mathematical expressions. OpenLabs provides a GUI with two dialog boxes. One box provides the existing physical models from the basic solver with the same format of the Lab, including the existing variables, constants, PDEs, source terms, diffusion coefficients, 5
equation of state, transport properties and boundary conditions/wall functions. The variables and constants can be used in the expressions of user-defined models. Moreover, the definition of existing objects can be copied to the Lab, so that it can be modified with an easy start. Figure 2 The OpenLabs GUI Once the Lab is prepared, it is transformed in a single mouse-click in the GUI and transparently to the user, into a C++ file and compiled as a dynamic library. Finally, the user-defined physical models will be plugged to the basic solver. 3. The underlying code OpenLabs relies on a modular CFD solver: the FINE /Open solver. It is a highly robust unstructured solver with a variety of models for turbulence, multiphase, combustion and radiation, providing altogether a highly professional quality assured CFD background. It covers a wide range of applications, from incompressible to supersonic and hypersonic, from perfect gas to liquids and condensable fluids, internal and external flows, fixed or rotating frames of references. The various basic CFD problem/objects are defined in the dedicated classes and prototyped by the existing physical models of the basic solver. Each class contains the 6
access through a dynamic pointer, which may point to either an internal function or an external function. The user-defined formulations will be written as the external functions and assigned to the object by OpenLabs. An un-limited number of objects of the class can be created internally (in the solver) or externally (in the user-defined library). Objects of the same type compose a doublelinked list. OpenLabs can access to each list to modify the existing object or add a new object. The solver has a modeled processor for each list. By looping over the lists, both the internal and external physical models will be processed with the assigned functions. 4. A detailed example: Actuator disk modeling Actuator disk models are often used in simulations of e.g. wind farms, ducted fans, propeller performance, to avoid the high computational cost to resolve the flow field around the rotating machinery. This section shows the example of an actuator disk model implemented in OpenLabs. It is shown how collaboration and free exchange of Labs can lead to more advanced models. Initially NUMECA created a Lab for a basic actuator disk model as already implemented in the free-surface flows dedicated environment FINE /Marin [1, 2]. The used model is based on non-iterative calculation of Stern et al. [3], the Hough and Ordway [4] circulation distribution with optimum type from Goldstein [5] without loading at the root and tip. The initial lab was written with a source term in the momentum equation in the X direction only. The cells for which the cell center coordinates are within the geometrical condition will account for the source term. The full set of theoretical expressions and their corresponding notation in a Lab can be found in Annex A. One may notice that the full Lab fits simply on one page. Constants and auxiliary terms are defined in a straightforward manner. They are used to define the non-differential expressions for the body force in axial and circumferential direction. Finally the body force in axial direction is added in this example as a source term to the momentum equation. This basic Lab was made available and Matt Anderson (The University of Sydney, Université Libre de Bruxelles) adapted the Lab to his application of four propellers in a duct as shown in figure 3. In addition to the loading profile as proposed in the initial Lab, a constant or linear loading was added by modifying the expression for the axial body force. 7
Figure 3 Actuator disk model applied to four propellers in a duct. Using symmetry only two propellers are modeled. 5. Example: Electric potential field Plasma actuators can be used to control the leading-edge separation [6]. It is made up of two electrodes separated by a dielectric material. A voltage is applied to the electrodes, which causes the air to ionize and results in body force acting on the flow. This body force can be computed based on the electric potential field. In this example, OpenLabs is used to solve an electric potential field around the airfoil of which a plasma actuator is installed at the leading edge. The governing equation is the Laplace equation given as, ( ) 0 2 Where, the permittivity 1. 0 for both fluid and solid. The electric potential is set to zero at far field boundaries and set to 1 and -1 at two electrodes. The full Lab can be found in Annex B. Figure 4 shows the isolines of the electric potential near the electrodes. 8
Figure 4 Electric potential isolines near leading edge of NACA 0021 airfoil. 6. Conclusions A new approach to Open CFD is proposed with emphasis on open and flexible access allowing easy collaboration. OpenLabs access is given to the variables, physical models, boundary conditions, fluid definition and transport properties of the underlying code FINE /Open. The ease of use and possibilities for collaboration are illustrated by the actuator disc example. The flexibility of NUMECA s approach to Open CFD is also reflected in a straightforward parallel access to benefit optimally from available hardware resources. 7. Acknowledgements The authors would like to express special thanks to Matt Anderson of ULB/The University of Sydney for his work on actuator disk modeling and sharing his work with the OpenLabs community. 8. References [1] User Manual, FINE /Open v2.12 (Including OpenLabs) Flow Integrated Environment, NUMECA International, Brussels, December 2012. [2] Theoretical Manual, ISIS-CFD, Ecole Centrale Nantes, CNRS, v3.0, June 2012. 9
[3] F. Stern, H. T. Kim, V. C. Patel, and H. C. Chen, A viscous flow approach to the computation of propeller-hull interaction, Journal of Ship Research, vol. 32, no. 4, pp. 246-262, 1988. [4] G. Hough and D. Ordway, The generalized actuator disk. Technical Report TAR-TR 6401, Therm Advanced Research Inc., 1964. [5] S. Goldstein, On the vortex theory of screws propellers, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 123, no. 792, pp. 440-465, 1929. [6] Orlov, D. M., Apker, T., He, C., Othman, H., and Corke, T. C., Modeling and experiment of Leading-edge Separation Control Using Single dielectric Barrier Discharge Plasma Actuators, AIAA-2007-0877, 2007. 10
Annex A. Actuator disk model =>CONSTANTS Constants: @Rp=0.01 Rp = Propeller radius @Rh=0.000 Rh = Hub radius @rpm=250 rpm = Rotation speed @delta=0.02 delta = Actuator disc thickness @Xpc=0.50 Xpc, Ypc, Zpc: @Ypc=0.05 Center coordinates of disc @Zpc=0.05 Uref = Reference velocity @Uref=10.0 L = Reference length @L=0.1 T0 = Prescribed force @T0=0.1 Q0 = Prescribed torque @Q0=0.0 @PI=3.14159265359 fbx and fbf = body forces normalized by * Uref 2 /L CT = thrust coefficient KQ = torque coefficient J = advance coefficient, n = rotations per second (rps), = the rotation speed, =>EQUATIONS @NONDIFFEXPR: Exprfbx ->EXPRESSION: fbx = IF(r<Rp AND xcoord>(xpc-delta*0.5) AND xcoord<(xpc+delta*0.5) ) \ Ax*rst*sqrt(1-rst) ELSE 0.0 @NONDIFFEXPR: Exprfbf ->EXPRESSION: fbf = IF(r<Rp AND xcoord>(xpc-delta*0.5) AND xcoord<(xpc+delta*0.5) ) \ Af*rst*sqrt(1-rst)/(rst*(1-rhprime)+rhprime) \ ELSE 0.0 =>SOURCETERMS @ SOURCE: sourcetomomx ->EXPRESSION: (fbx) * (Rho*Uref*Uref/L) ->AddToExistingPde: MomentumXEquation =>AUXTERMS @r=sqrt((ycoord-ypc)*(ycoord-ypc)+(zcoord-zpc)*(zcoord-zpc)) @n=rpm/60. @Dp=2.0*Rp @J=Uref/(n*Dp) @Rho=Density @CT=2*T/(Rho*Uref*Uref*PI*Rp*Rp) @KT=T/(Rho*n*n*Dp*Dp*Dp*Dp) @KQ=Q/(Rho*n*n*Dp*Dp*Dp*Dp*Dp) @rprime=r/rp @rhprime=rh/rp @aux=105./((4.0+3.0*rhprime)*(1.0-rhprime))/delta @rst=(rprime-rhprime)/(1.0-rhprime) @T=T0 @Q=Q0/T0*T @Ax=CT*aux/16. @Af=KQ*aux/(J*J*PI) 11
Annex B. Electric potential field External =>EQUATIONS @PDE: potential ->EXPRESSION: 0 = DIFF(permittivity_air) ->VARIABLE_NAME: phi ->UseCustomBC: elec_n, electroden ->UseCustomBC: elec_ext, inlet,out ->UpperLimit: 1.0 ->LowerLimit: -1.0 ->IMPLICIT_BLENDING: 1.0 ->IMPLICIT_SOR: 1.0 =>CUSTOM_BOUNDARY_CONDITIONS @CUSTOMIZED_BOUNDARY_CONDITION: elec_n ->EXPRESSION: -1.0 @CUSTOMIZED_BOUNDARY_CONDITION: elec_ext ->EXPRESSION: 0.0 =>ALGEBRAIC_DIFFUSION_COEFFICIENTS @ALGDIFFCOEFF: permittivity_air ->EXPRESSION: 1.0 Airfoil =>EQUATIONS @PDE: potential ->EXPRESSION: 0 = DIFF(permittivity_sol) ->VARIABLE_NAME: phi ->UseCustomBC: elec_s, electrodes ->UseCustomBC: elec_n, electroden ->UpperLimit: 1.0 ->LowerLimit: -1.0 ->IMPLICIT_BLENDING: 1.0 ->IMPLICIT_SOR: 1.0 =>CUSTOM_BOUNDARY_CONDITIONS @CUSTOMIZED_BOUNDARY_CONDITION: elec_s ->EXPRESSION: 1.0 @CUSTOMIZED_BOUNDARY_CONDITION: elec_n ->EXPRESSION: -1.0 =>ALGEBRAIC_DIFFUSION_COEFFICIENTS @ALGDIFFCOEFF: permittivity_sol ->EXPRESSION: 1.0 12