The paper presents a prediction method for the flowfield and surface pressure distribution induced by three-dimensional jets injected from a flat surface into a crossflow. An eddy viscosity model extended from Prandtl's concept has been developed to account for the curved nature of the jets with arbitrary cross-sectional shape. The first-order influence of the fluctuating nature of the turbulent flow is reflected via axial turbulence information. The Reynolds-averaged, Navier-Stokes equations are solved using the finite-element method, and the penalty function method is used to discretize the pressure in a consistent manner. The eight-noded, isoparametric finite element is used to approximate the computational domain and the field variables. The performance of the present prediction method is verified for a single circular jet in a crossflow at R = 4, which has enough measured data available for detailed comparisons. The jet trajectory and axial velocity decay comparison are excellent, and the surface pressure distribution is well predicted except for the wake region right behind the jet. The same methodology is then applied to single-and dual-rectangular jets in a crossflow at the same velocity ratio, and most of the important features of the surface pressure distribution are predicted well. The general observation is that the entrainment process due to the turbulent mixing is modeled reasonably through a generalized eddy viscosity concept supported by an axial turbulence intensity correlation, and the agreement achieved here between the prediction and existing measured data is considered good for a three-dimensional, turbulent flow of this complexity.a b D f fi L Nomenclature = constant, = I/.53 = shear layer width = averaged jet half width = constant = pressure coefficient = diameter, = Dj -D eq --proportionality factor for eddy viscosity = vector of body forces = streamwise length of the rectangular nozzle = length of the potential core = direction normal to the boundary = static pressure = dynamic pressure = jet-to-crossflow velocity ratio = vector of surface traction = mean velocity components = maximum velocity = axial velocity = fluctuating velocity components = Reynolds shear stress in xy plane = Cartesian coordinates = angle between the jet axis and x axis F = boundary of the computation domain d = variational symbol dij = Kronecker delta e = penalty parameter (JL T = eddy viscosity V T = kinematic eddy viscosity 12 = bounded computation domain tp -element interpolation function for velocity p = density of the fluid = element interpolation function for pressure £ ,£",17 = intrinsic coordinates [c] -element gradient matrix [f] -element force vector [F] = global force vector matrix [k] -element stiffness [K] = global stiffness matrix [m] = element pressure mass matrix \p] = nodal pressure vector in an element («] = nodal velocity vector in an element [U] = column vector of velocity unknown
