Jeffrey C. Tromp

A Volterra kernel identification scheme applied to aerodynamic reactions

Jeffrey C. Tromp Jerry Jenkins

Kernel (algebra)

Identification

Volterra series

10.2514/6.1990-2803

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Citations (21)

Flowfield Simulation About a 65-Degree Delta Wing During Constant Roll-Rate Motions

Journal of Aircraft (1999)

Jeffrey C. Tromp

Numerical simulations of the flowfield over a 65-degree delta wing undergoing constant roll-rate maneuvers are presented. The unsteady, three-dimensional, full Navier-Stokes equations are solved using a BeamWarming implicit algorithm. Computations are performed for two distinct maneuvers. The first is a constant-rate coning motion, with resulting body-axis moments compared to rotary data from the AFRL vertical wind tunnel. The second is a constant roll-rate, barrel-roll type maneuver with zero pitch and yaw rates. In both maneuvers the angle of attack and sideslip angle are fixed at 30 degrees and zero degrees respectively. Vortex breakdown locations and aerodynamic reactions for these motions are compared to quantify angular rate effects and their impact on recent aerodynamic modeling efforts. Nomenclature

Delta wing

Constant (computer programming)

Degree (music)

10.2514/2.2462

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Citations (0)

Engineering calculation methods for viscous/inviscid interaction flows

A.A. Halim Jeffrey C. Tromp

Inviscid flow

Source

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Numerical study of three viscous/inviscid interaction methods

Mathematical Systems Theory (1988)

Jeffrey C. Tromp

Inviscid flow

Finite difference

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Temporal evolution of three-dimensional vortex breakdown from steady, axisymmetric solutions

AIAA Journal (1996)

Jeffrey C. Tromp Philip Beran

HE emergence and consequences of asymmetries in swirling flows that are initially steady and axisymmetric are examined. The strength of an isolated vortex in a tube is increased in a parametric fashion through a critical value, where stability to three-dimensional disturbances is lost. The flow behavior undergoes a bifurcation at the critical value from steady and axisymmetric flow to unsteady and three-dimensional flow. Other computations of bifurcation phenomena in swirling flows have been presented by Leibovich and Kribus,1 Reran and Culick,2 and Lopez.3 These works are limited to bifurcations that only involve axisymmetric flows. Axisymmetric base flows serve as initial conditions to a threedimensional time-integration algorithm. The minimum axial velocity component Q (t) is computed and compared with the initial value. Of particular interest is the characterization of the stability loss and the relationship between the appearance of asymmetries and the associated changes in Q. The computational approach is as follows. First, a pseudoarclength continuation (PAC) algorithm2 provides the steady, axisymmetric initial condition for a specified vortex strength V. The Mach number M and Reynolds number Re (based on vortex core radius) are held fixed at 0.3 and 2.5 x 102, respectively. No nonunique axisymmetric solutions are found at Re — 2.5 x 10 2, consistent with Ref. 2. The two-dimensional solution is then interpolated onto the three-dimensional mesh using a fourth-order-accurate cubic spline scheme.4 Then time integration is carried out by the time-accurate Navier-Stokes (TANS) model. The TANS model is a special-purpose, time-integration algorithm developed specifically for this work and is described in Ref. 5. The TANS model employs fourth-order compact, or Fade, operators6 to discretize spatial derivatives, thus allowing for fewer grid nodes while maintaining sufficient accuracy. A multiblock grid is used to allow for a nearly rectilinear arrangement of nodes near the tube centerline, while near orthogonality is maintained at the tube wall. The PAC algorithm is implemented with the same boundary conditions and tube geometry as the TANS model, using a simple algebraic grid. The physical domain consists of a two-stage cylindrical tube of circular cross section and varying radius.2 The first stage contains a constriction that controls the upstream movement of the breakdown region. The tube radius (nondimensionalized by vortex core radius) at the inlet station is fixed at /? 0 = 2. The number of nodes in the computational coordinate directions are (nx, ny, nz), where nx defines stream wise spacing and ny and nz are equal and define cross-plane spacing in the y and z directions, respectively. Three grids are employed in this work. Grid Gl consists of 98 x 41 2 nodes, grid G2 contains 122 x 612 nodes, and grid G3 uses 146 x 412

10.2514/3.13117

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Citations (6)

The role of nonunique axisymmetric solutions in 3-D vortex breakdown

Physics of Fluids (1997)

Jeffrey C. Tromp Philip Beran

The three-dimensional, compressible Navier–Stokes equations in primitive variables are solved numerically to simulate vortex breakdown in a constricted tube. Time integration is performed with an implicit Beam-Warming algorithm using fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier–Stokes equations with Newton’s method. The effects of three-dimensionality on flows that are initially axisymmetric and stable to 2-D disturbances are examined. Stability of the axisymmetric base flow is assessed through 3-D time integration. Axisymmetric solutions at a Mach number of 0.3 and a Reynolds number of 1000 contain a region of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies the appearance of critical flow (a flow that can support an axisymmetric standing wave), the solutions bifurcate into 3-D time-periodic flows. Thus this numerical study shows that the vortex strength associated with the loss of stability to 3-D disturbances and that of the primary limit point are in close proximity. Additional numerical and theoretical studies of 3-D swirling flows are needed to determine the impact of various parameters on dynamic behavior. For example, it is possible that a different flow behavior, leading to a nearly axisymmetric vortex breakdown state, may develop with other inlet profiles and tube geometries.

Compressible flow

10.1063/1.869194

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Citations (20)

The Dependence of the Time-Asymptotic Structure of 3-D Vortex Breakdown on Boundary and Initial Conditions.

Jeffrey C. Tromp

Abstract : The three-dimensional, compressible Navier-Stokes equations are solved numerically to simulate vortex breakdown in tubes. Time integration is performed with an implicit Beam-Warming algorithm, which uses fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier-Stokes equations using Newton's method. Stability of the axisymmetric initial conditions is assessed through 3-D time integration. Unique axisymmetric solutions at a Reynolds number of 250 lose stability to 3-D disturbances at a critical value of vortex strength, resulting in 3-D and time-periodic flow. Axisymmetric solutions at a Reynolds number of 1000 contain regions of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique, axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies critical flow, the solutions bifurcate into 3-D periodic flows.

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Citations (2)

Temporal evolution of three-dimensional vortex breakdown from steady, axisymmetric solutions

2018 Fluid Dynamics Conference (1995)

Jeffrey C. Tromp Philip Beran

HE emergence and consequences of asymmetries in swirling flows that are initially steady and axisymmetric are examined. The strength of an isolated vortex in a tube is increased in a parametric fashion through a critical value, where stability to three-dimensional disturbances is lost. The flow behavior undergoes a bifurcation at the critical value from steady and axisymmetric flow to unsteady and three-dimensional flow. Other computations of bifurcation phenomena in swirling flows have been presented by Leibovich and Kribus,1 Reran and Culick,2 and Lopez.3 These works are limited to bifurcations that only involve axisymmetric flows. Axisymmetric base flows serve as initial conditions to a threedimensional time-integration algorithm. The minimum axial velocity component Q (t) is computed and compared with the initial value. Of particular interest is the characterization of the stability loss and the relationship between the appearance of asymmetries and the associated changes in Q. The computational approach is as follows. First, a pseudoarclength continuation (PAC) algorithm2 provides the steady, axisymmetric initial condition for a specified vortex strength V. The Mach number M and Reynolds number Re (based on vortex core radius) are held fixed at 0.3 and 2.5 x 102, respectively. No nonunique axisymmetric solutions are found at Re — 2.5 x 10 2, consistent with Ref. 2. The two-dimensional solution is then interpolated onto the three-dimensional mesh using a fourth-order-accurate cubic spline scheme.4 Then time integration is carried out by the time-accurate Navier-Stokes (TANS) model. The TANS model is a special-purpose, time-integration algorithm developed specifically for this work and is described in Ref. 5. The TANS model employs fourth-order compact, or Fade, operators6 to discretize spatial derivatives, thus allowing for fewer grid nodes while maintaining sufficient accuracy. A multiblock grid is used to allow for a nearly rectilinear arrangement of nodes near the tube centerline, while near orthogonality is maintained at the tube wall. The PAC algorithm is implemented with the same boundary conditions and tube geometry as the TANS model, using a simple algebraic grid. The physical domain consists of a two-stage cylindrical tube of circular cross section and varying radius.2 The first stage contains a constriction that controls the upstream movement of the breakdown region. The tube radius (nondimensionalized by vortex core radius) at the inlet station is fixed at /? 0 = 2. The number of nodes in the computational coordinate directions are (nx, ny, nz), where nx defines stream wise spacing and ny and nz are equal and define cross-plane spacing in the y and z directions, respectively. Three grids are employed in this work. Grid Gl consists of 98 x 41 2 nodes, grid G2 contains 122 x 612 nodes, and grid G3 uses 146 x 412

10.2514/6.1995-2310

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Citations (5)

Flowfield simulation about a 65-degree delta wing during constant roll-rate motions

Jeffrey C. Tromp

Numerical simulations of the flowfield over a 65-degree delta wing undergoing constant roll-rate maneuvers are presented. The unsteady, three-dimensional, full Navier-Stokes equations are solved using a BeamWarming implicit algorithm. Computations are performed for two distinct maneuvers. The first is a constant-rate coning motion, with resulting body-axis moments compared to rotary data from the AFRL vertical wind tunnel. The second is a constant roll-rate, barrel-roll type maneuver with zero pitch and yaw rates. In both maneuvers the angle of attack and sideslip angle are fixed at 30 degrees and zero degrees respectively. Vortex breakdown locations and aerodynamic reactions for these motions are compared to quantify angular rate effects and their impact on recent aerodynamic modeling efforts. Nomenclature

Delta wing

Constant (computer programming)

Degree (music)

10.2514/6.1998-4453

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Citations (1)

Jeffrey C. Tromp

Papers

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