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58963) TRANSONIC AERODYNAMICS NUMERICAL ANALYSIS , Petrović Z. , Stupar S. , Mechanical Engineering Faculty University of Belgrade 1996 ; Contents : 1 Introduction 1.1 Preliminary Remarks. 1.2 Governing Equations 1.3 Simplifications to the Governing Equations 1.3.1 Definition of an Adiabatic Flow. 1.3.2 Definition of an Irrotational Flow 1.3.3 Crocco`s Theorem 1.3.4 Isentropic Gas Relation 1.4 Algebraic Form of Energy Equation for Steady Adiabatic Flow 1.5 The Isentropic Form of the Energy Equation 1.6 The Momentum Conservation Laws. 1.7 Isentropic Shocks vs. `Real World Shocks` 1.7.1 Rankine-Hugoniot approach 1.7.2 Isentropic approach 1.8 Techniques for Handling Shocks in Potential Flow Calculations 1.9 Summary 2 Transonic Small Disturbance Equation 2.1 Preliminary Remarks. 2.1.1 Treatment of Flow Angle of Attack 2.2 Definition of Disturbance Potential 2.3 Boundаry Conditions for Flow at the Body Surface 2.4 Derivation of the TSD Equation 2.5 Properties of the TSD Equation. 2.6 Finite Difference Terminology 2.7 Conservation Form vs. Non-Conservation Form 2.8 Finite Difference Expression Form of the TSD Equation in Subsoni 2.9 Murman-Cole Switching in supersonic Regions 2.10 Discretization Error Associated with Equation (2.2) 2.11 Loss of Conservation Property due to Switching 2.12 Murman-Cole Switching in Conservation Form 2.13 Application of Boundary Conditions 2.13.1 Region Ahead of the Leading Edge: (1 2.13.2 Region of the Slit: (ILE SITE) 2.13.3 Region Downstream of the Trailing Edge: (ITE << Imax 2.14 Far Field Boundary Conditions 2.15 Relaxation Procedure for the TSD Equation 2.15.1 Gauss-Seidel Scheme 2.16 The Point Successive Over-Relaxation (SOR) Scheme 2.17 The Line Gauss-Seidel Iteration Scheme 2.18 The Thomas Algorithm 2.19 Solution of the SLOR Scheme to TSD Equation 2.20 Summary 3 The Transonic Full Potential Equation 3.1 Introduction 3.2 Jameson`s Rotated Difference Scheme 3.3 Transformation of the Continuity Equation to a Curvilinear Coordina System. 3.4 Boundary Conditions. 3.4.1 Boundary Condition at the Solid Surface 3.4.2 Boundary Conditions at the Far Field... 3.5 Governing Equation for Axisymmetric Flows in the Transformed Plan 3.6 Construction of the Body-Fitted Coordinate system... 3.6.1 H-grid, algebraic approach 3.6.2 O-grid, algebraic approach. 3.7 Construction of C-Grids Around Airfoils 3.8 Generation of the Orthogonal Grid... 3.9 Discretization of the Governing Equation 3.10 Computation of Metrics at Half Points 3.11 Computation of Densities and Contravariant Velocities.. 3.12 Relaxation Procedure for Solving the Full Potential Equation 3.12.1 Interior Points 3.13 Summary 4 Numerical Technique for Designing Airfoils 4.1 Introduction. 4.2 Optimization Approach 4.2.1 Design Objective 4.2.2 Design Point 4.2.3 Starting Point. 4.2.4 Design Variables 4.2.5 Design Constraints 4.2.6 Black Box. 4.3 CONMIN to Black Box Coupling. 4.3.1 Optimization Process 4.4 Inverse Design Techniques. 4.5 Carlson`s Inverse Design Technique.. 5 Unsteady Transonic Potential Flow 5.1 Introduction. 5.2 Governing Equations 5.3 Unsteady Transonic Small Disturbance Equation 5.4 Boundary Conditions. 5.5 Low-Frequency Approximation 5.6 Characteristic of the Low-Frequency Transonic Small Disturbance Equation. 5.7 Discretization of the Low-Frequency Small-Disturbance Equation. A Solution of the diagonal system of equations A.1 Three diagonal Equation System A.2 Quad-Diagonal Matrix System B Selected Papers paperback, size 20,5 x 29 cm , English , 152 pages