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Nozzle Definition
A large number of parameters is required to fully define the nozzle including geometries and materials of each component. Each parameter must be specified in the config file although its value will be overwritten if it is specified as a design variable.
The inner wall is parameterized using a 3rd degree B-spline. It is specified by the WALL keyword and a vector of B-spline coefficient coordinates WALL_COEFS, ordered x-coordinate first, then r-coordinate. The WALL_COEFS_DV vector is the same size as WALL_COEFS and is used to specify which coefficient coordinates are design variables. See the design variable section for more details. For example:
WALL= (BSPLINE)
WALL_COEFS= (0.0000, 0.0000, 0.1500, 0.1700, 0.1900, 0.2124, 0.2269, 0.2734, 0.3218, 0.3218, 0.3230, 0.3343, 0.3474, 0.4392, 0.4828, 0.5673, 0.6700, 0.6700, 0.3255, 0.3255, 0.3255, 0.3255, 0.3255, 0.3238, 0.2981, 0.2817, 0.2787, 0.2787, 0.2787, 0.2797, 0.2807, 0.2936, 0.2978, 0.3049, 0.3048, 0.3048)
WALL_COEFS_DV= (0, 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 11, 0, 0, 0, 0, 0, 12, 13, 14, 15, 15, 15, 16, 17, 18, 19, 20, 21, 21)
In the above case, there are 18 coefficients. It is important that the first two and last two have the same x and r coordinates. In addition, there is a duplicated coordinate near the throat to ensure good behavior during optimization.
Wall layers are defined in order by number starting with LAYER1, then LAYER2 and so on, from innermost to outermost. Each layer definition follows this format:
LAYER#= (LAYER-NAME, LAYER-GEOMETRIC-PARAMETERIZATION, LAYER-MATERIAL-NAME)
For example, the inner thermal layer of the nozzle can be defined as:
% Inner thermal layer takes the heat load
LAYER1= (THERMAL_LAYER, PIECEWISE_LINEAR, CMC)
LAYER1_THICKNESS_LOCATIONS= (0, 0.3, 0.6, 1.0)
LAYER1_THICKNESS_VALUES= (0.03, 0.03, 0.03, 0.03)
LAYER1_DV= (0, 1, 2, 0, 3, 4, 5, 6)
where it is given the name THERMAL_LAYER, defined with a piecewise-linear geometry and associated with the CMC (ceramic matrix composite) material definition.
A piecewise-linear geometry must have the locations of its breaks and the value at those breaks defined. The keyword LAYER#_THICKNESS_LOCATIONS is used to define a vector of normalized break locations (normalized by nozzle length) and the keyword LAYER#_THICKNESS_VALUES is used to define a vector of values at each break location, as seen above.
The LAYER#_DV keyword is used to specify which break locations and values are design variables. The first half of the entries in the LAYER#_DV vector correspond to the break locations and the second half correspond to the break values. See the design variable page for more information.
A constant thickness layer is defined using the CONSTANT layer geometric parameterization keyword. An additional keyword, LAYER#_THICKNESS is required to define the thickness of the layer, for example:
% Air gap between thermal and load layers
LAYER2= (AIR_GAP, CONSTANT, AIR)
LAYER2_THICKNESS = 0.005
The baffles (vertical structural panels perpendicular to the nozzle axis) are defined by specifying the number and material used with the BAFFLE keyword, along with definitions of normalized x-coordinate location, thickness and height. By default, currently baffle heights are resized to mate with the external aircraft geometry which is hard-coded in MULTI-F, so the provided height values are ignored. An example baffle specification is below:
BAFFLES= (6,PANEL)
BAFFLES_LOCATION= (0, 0.2, 0.4, 0.6, 0.8, 1)
BAFFLES_THICKNESS= (0.01, 0.01, 0.01, 0.01, 0.01, 0.01)
BAFFLES_HEIGHT= (0.2, 0.2, 0.2, 0.2, 0.2, 0.2)
BAFFLES_DV= (0, 1, 2, 3, 4, 0, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 0)
where 6 baffles are defined using the PANEL material. The BAFFLES_DV keyword is used to specify which baffle locations, thicknesses, and heights are design variables, in that order. See the design variables page for more information.
The stringers (long thin members running the length of the nozzle) are defined by specifying the number (assumed to be spaced by equal angle) and material used with the STRINGERS keyword. Currently a piecewise-linear geometry is assumed for both the stringer thickness (circumferential direction) and height (radial direction). The stringer thickness and height geometry definitions share the same non-dimensional break locations which are specified in the STRINGERS_BREAK_LOCATIONS keyword. Height and thicknesses are defined in the vectors provided with the STRINGERS_HEIGHT_VALUES and STRINGERS_THICKNESS_VALUES keywords. A STRINGERS_DV keywords can be provided to specify which break locations, height values, and thickness values are design variables, in that order. See the design variables page for more information. An example stringer parameterization is:
STRINGERS= (4,GR-BMI)
STRINGERS_BREAK_LOCATIONS= (0, 0.2, 0.4, 0.6, 0.8, 1)
STRINGERS_HEIGHT_VALUES= (0.01, 0.01, 0.01, 0.01, 0.01, 0.01)
STRINGERS_THICKNESS_VALUES= (0.01, 0.01, 0.01, 0.01, 0.01, 0.01)
STRINGERS_DV= (0, 1, 2, 3, 4, 0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
It is common to specify that the stringers height coincides with the baffle height. In this case the BAFFLES_LOCATION string can be provided instead of a vector for the STRINGERS_BREAK_LOCATIONS keyword and the BAFFLES_HEIGHT string can be provided instead of a vector for the STRINGERS_HEIGHT_VALUES keyword. In this case, STRINGERS_DV should not be specified. For example:
STRINGERS= (4,GR-BMI)
STRINGERS_BREAK_LOCATIONS= BAFFLES_LOCATION
STRINGERS_HEIGHT_VALUES= BAFFLES_HEIGHT
STRINGERS_THICKNESS_VALUES= (0.01, 0.01, 0.01, 0.01, 0.01, 0.01)
Materials are defined in order by number starting with MATERIAL, then MATERIAL2 and so on in no particular order. They are associated with different components using their defined name. Each material definition follows this format:
MATERIAL1# = (MATERIAL-NAME, MATERIAL-TYPE)
where MATERIAL_NAME is a descriptive string and MATERIAL_TYPE is either ISOTROPIC, ANISOTROPIC_SHELL, or FIXED_RATIO_PANEL. Material properties are defined using the keyword MATERIAL#_MATERIAL-PROPERTY-NAME. Some material properties require multiple values.
Isotropic materials have the same properties in all directions, therefore only one value need be provided for each material property. An example comprehensive definition of an isotropic material is:
MATERIAL1= (CMC, ISOTROPIC)
MATERIAL1_DENSITY= 2410
MATERIAL1_ELASTIC_MODULUS= 67.1e9
MATERIAL1_POISSON_RATIO= 0.33
MATERIAL1_THERMAL_CONDUCTIVITY= 1.41
MATERIAL1_THERMAL_EXPANSION_COEF= 0.24e-6
MATERIAL1_PRINCIPLE_FAILURE_STRAIN= 0.0007
MATERIAL1_MAX_SERVICE_TEMPERATURE= 973
Anisotropic-shell materials have different properties in different directions but also assume a very thin material. Some properties can take multiple values; if only one value is provided it will be duplicated for all directions in the material. An example comprehensive definition of an anisotropic-shell material is:
MATERIAL2= (GR-BMI, ANISOTROPIC_SHELL)
MATERIAL2_DENSITY= 1568
MATERIAL2_ELASTIC_MODULUS= (60e9, 60e9)
MATERIAL2_SHEAR_MODULUS= 23.31e9
MATERIAL2_POISSON_RATIO= 0.344
MATERIAL2_MUTUAL_INFLUENCE_COEFS= (0.0, 0.0)
MATERIAL2_THERMAL_CONDUCTIVITY= (3.377, 3.377, 3.414)
MATERIAL2_THERMAL_EXPANSION_COEF= (1.2e-6, 1.2e-6, 0.0)
MATERIAL2_LOCAL_FAILURE_STRAIN= (0.0075, -0.0052, 0.0075, -0.0052, 0.0017)
%MATERIAL2_YIELD_STRESS= 324e6
MATERIAL2_MAX_SERVICE_TEMPERATURE= 505
Properties with two values assume the first is in the local tangential direction, and the second is in the local circumferential direction, i.e. (E1, E2). Thermal conductivity is provided three values, one for each axis in the local coordinate system (tangential, circumferential, radial, i.e. k1, k2, k3). Thermal expansion coefficient is provided three values, the first two correspond to normal components in the local coordinate system in the plane of the shell (alpha1, alpha2) and the last corresponds to the shear component in the plane of the shell (alpha12). Local failure strain is provided 5 components: (tensile failure strain in direction 1, compressive failure strain in direction 1, tensile failure strain in direction 2, compressive failure strain in direction 2, shear failure strain).
A fixed-ratio panel material is a panel of predifined material layers where each layer has a fixed ratio of layer thickness to total panel thickness. The purpose of this material definition is to simplify the material definition for the baffles which are assumed to be constructed from a sandwich-style material. A fixed-ratio panel material is defined specifying the material names of each layer and the ratio of each layer to the total panel thickness. Since it is composed of multiple materials each with different stress failure criteria, a single stress failure criterion can be associated with it. For example:
MATERIAL4= (PANEL, FIXED_RATIO_PANEL)
MATERIAL4_LAYERS= (GR-BMI, TI-HC, GR-BMI)
MATERIAL4_THICKNESS_RATIOS= (0.2, 0.6, 0.2)
MATERIAL4_YIELD_STRESS= 324e6
Note that GR-BMI and TI-HC are names of materials previously defined. The sandwich construction of the panel is such that there is a 20% thick GR-BMI layer followed by a 60% thick TI-HC layer followed again by a 20% thick GR-BMI layer.