VNAP2: a computer program for computation of two-dimensional, time-dependent, compressible, turbulent flow

Cline, M. C.

doi:10.2172/5507314

Cited by 31 publications

(12 citation statements)

References 1 publication

(1 reference statement)

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“…However, there are only five independent governing equations [i.e., Eqs. (1)(2)(3)(4)(5)]. Consequently, only five of the infinite number of compatibility relations are independent.…”

Section: Kentzer's Methodsmentioning

confidence: 99%

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Three-dimensional flow in rotating rocket motor nozzles

Brown

Hoffman

1986

Journal of Spacecraft and Rockets

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A procedure used to calculate the effects of rocket motor rotation on the subsonic/transonic flowfield in axisymmetric rocket motor nozzles is presented. The governing equations for the unsteady three-dimensional flow of an ideal, in viscid fluid in thermodynamic equilibrium are derived in a noninertial reference frame. The governing equations are integrated numerically using MacCormack's explicit finite difference method. The boundary conditions are applied using Kentzer's method. The present technique is used to provide an accurate, steady, supersonic, initial-value surface for an existing method-of-characteristics analysis for steady three-dimensional supersonic flow. The steady supersonic initial-value surface is obtained as the asymptotic solution for large time of the unsteady subsonic/transonic flow analysis. This procedure can also be used to calculate the effects of inlet flow misalignment on the subsonic/transonic flowfield in nozzles. NomenclatureM =Mach number p = static pressure r L 0,z = coordinates R, f -position vectors, inertial and noninertial reference frames, respectively t = time v_ = velocity component V -velocity vector X = body force vector p = density oj = angular acceleration vector Subscripts M = relative to the missile TV = relative to the nozzle r,0,z -components XYZ, xyz = inertial and noninertial reference frames, respectively IntroductionT HE objective of this investigation 1 ' 2 was to develop an analysis and a computer program to predict the unsteady three-dimensional subsonic/transonic flowfields that occur in the inlets and throats of axisymmetric rocket motor nozzles, including the effects of rotation and inlet flow misalignment. The results of the present method can be used to provide an accurate steady supersonic initial-value surface (IVS) for an existing method-of-characteristics (MOC) analysis of the steady supersonic flowfield in the diverging portion of the nozzle. 3 One technique for generating the maneuvering torque for a fast response system is to rotate the supersonic portion of the propulsive nozzle to create a thrust misalignment and a corresponding turning torque. In the analysis of such a system, two questions arise: 1) how much missile turning torque is generated by a specified amount of nozzle rotation, and 2)

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“…However, there are only five independent governing equations [i.e., Eqs. (1)(2)(3)(4)(5)]. Consequently, only five of the infinite number of compatibility relations are independent.…”

Section: Kentzer's Methodsmentioning

confidence: 99%

“…(1)(2)(3)(4)(5), are singular on the centerline (r = Q). Consequently, as suggested by Reyhner, 11 the Cartesian forms of the governing equations were employed to obtain the solution on the centerline.…”

Section: Centerline Pointsmentioning

confidence: 99%

Three-dimensional flow in rotating rocket motor nozzles

Brown

Hoffman

1986

Journal of Spacecraft and Rockets

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“…Details of transformations of the governing equations are given in Ref. 5. Briefly, the grid points in the computational domain are computed using the 1969 explicit, unsplit MacCormack scheme 11 which alternately uses backward and forward finite differences for the predictor and corrector steps.…”

Section: Methodsmentioning

confidence: 99%

Simulation of Starting Transients in the UTSIMHD Generator

et al. 1983

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A numerical procedure for solving the unsteady, two-dimensional, compressible Navier-Stokes equations has been extended for magnetohydrodynamic (MHD) flows by the inclusion of the appropriate Lorentz force and Joule heating terms in the governing equations. With appropriate initial and boundary conditions, the procedure can be used for the investigation of transient phenomena as well as the asymptotic steady-state characteristics of internal MHD flows. Results obtained for the simulation of starting processes in the UTSI coal-fired MHD flow train are presented and found to be in good agreement with experimental observations. NomenclatureA = cross-sectional area of the channel, m 2 a = local speed of sound, m/s B = magnetic field, T E = electrical field, V/m h = height of the channel (in y direction), m I L = load current, A I s = local short circuit current, A ij = lead-out current in they th frame, A / = current density, A/m 2 L = channel length, m / = mixing length, m P = electrical power, W Pr = Prandtl number p = static pressure, N/m 2 RJ = resistance of theyth ballast resistor, 0 R L = load resistance, Q Rf = resistance per unit length of the channel, 0/m r = internal resistance of the plasma, 12 S = one electrode pitch, m T = static temperature, K u = velocity in x direction, m/s u r = wall friction velocity, m/s V d = voltage drop, V v = velocity in y direction, m/s x,y, t = physical space coordinates j3 = Hall parameter 7 = specific heat ratio <5 = boundary-layer thickness, m £ y. r = computational space coordinates 0 = diagonalization angle K = thermal conductivity, W/m • K X = second coefficient of viscosity, N • s/m 2 fji = molecular viscosity, N • s/m 2 v = kinematic viscosity, m 2 /s p = density, kg/m 3 a = electrical conductivity, S/m T = shear stress, N/m 2 $ = electrical potential function, V ty = current stream function, A/m

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“…The solution at each boundary point was obtained by employing the method of reference plane characteristics. This method was applied in previous works to both interior and boundary points and was found to be very accurate for predicting solutions at the boundaries; see references [9] to [11]. The choice of the reference plane used for each boundary was such that, at least, one of the characteristic curves lies inside the computational domain.…”

Section: Boundary Conditions and Time Regulationmentioning

confidence: 99%

“…This method solves the unsteady equations in nonconservation forms, and the solution is advanced in consecutive time levels until the steady state solution is obtained ( as hoposcotch method does). For more details of the applications of the method, the reader is referred to references [9] to [11].…”

Section: Boundary Conditions and Time Regulationmentioning

confidence: 99%

Application of Hoposcotch Method for Solving the Unsteady Two Dimensional, Inviscid, Internal Flows

Kemry

1989

International Conference on Aerospace Sciences and Aviation Tec

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In the present study, the hoposcotch method was tested for solving the axisymmetric, inviscid, compressible, shock-free flows. The physical space was transformed into a rectangular computational space. Hoposcotch method was applied to solve the unsteady, cylindrical, conserved governing equations of motion in the transformed computational space, with the steady state solution computed as the asymptote of the transient solution. The source flow and the transonic flow through a converging-diverging nozzle were considered as test problems. The solutions were compared with the available exact, experimental, and numerical results.

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VNAP2: a computer program for computation of two-dimensional, time-dependent, compressible, turbulent flow

Cited by 31 publications

References 1 publication

Three-dimensional flow in rotating rocket motor nozzles

Three-dimensional flow in rotating rocket motor nozzles

Simulation of Starting Transients in the UTSIMHD Generator

Application of Hoposcotch Method for Solving the Unsteady Two Dimensional, Inviscid, Internal Flows

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