Non-uniform slot injection (suction) or wall enthalpy into a steady nonsimilar compressible laminar boundary layer
TL;DR: In this paper, the effect of different free stream Mach number on the point of separation of nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and wall enthalpy has been studied from the starting point of the streamwise co-ordinate to the exact position of separation.
Abstract: Steady two-dimensional and axisymmetric compressible nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and non-uniform wall enthalpy have been studied from the starting point of the streamwise co-ordinate to the exact point of separation. The effect of different free stream Mach number has also been considered. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is observed that the non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise co-ordinate has very little effect on the skin friction and thus on the point of separation.
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TL;DR: In this article, an analysis is performed to obtain the non-similar solution of a steady compressible laminar boundary layer flow over a yawed infinite circular cylinder with non-uniform slot injection (or suction) and nonuniform wall enthalpy, where the difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme.
Abstract: An analysis is performed to obtain the non-similar solution of a steady compressible laminar boundary layer flow over a yawed infinite circular cylinder with non-uniform slot injection (or suction) and non-uniform wall enthalpy. The difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite-difference scheme. It is observed that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the reverse. An increase in Mach number and total enthalpy at wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) has very little effect on the skin friction and hence on the point of separation.
27 citations
TL;DR: In this article, the numerical difficulties are overcome by applying the method of quasi-linear implicit finite difference scheme with an appropriate selection of finer stepsize along the streamwise direction, and the non-uniform wall enthalpy at the wall has very little effect on the skin frictions or the point of separation.
Abstract: Steady non-similar laminar compressible boundary layer flows over yawed infinite cylinder with non-uniform multiple slot injection/suction and non-uniform wall enthalpy have been studied. The numerical difficulties are overcome by applying the method of quasi-linear implicit finite difference scheme with an appropriate selection of finer stepsize along the streamwise direction. Separation can be delayed more effectively by non-uniform multiple slot suction and also by moving the slots downstream as compared to the non-uniform single slot suction but the non-uniform multiple slot injection has the reverse effect. Increase of Mach number shifts the point of separation upstream due to the increase in the adverse pressure gradient. An increase of enthalpy at the wall causes separation to occur earlier while cooling delays it. Non-uniform total enthalpy at the wall has very little effect on the skin frictions or the point of separation. Also, the yaw angle has very little effect on the location of the point of separation.
18 citations
TL;DR: In this article, the effect of non-uniform slot injection/suction and total enthalpy at the wall for a steady non-similar laminar compressible boundary layer flow over a rotating sphere is presented.
Abstract: A study for the effect of non-uniform slot injection/suction and non-uniform total enthalpy at the wall for a steady non-similar laminar compressible boundary layer flow over a rotating sphere is presented. The effects of rotation and free stream Mach number have also been considered. Non-similar solutions have been obtained from the starting point of the stream wise coordinate to the point of separation using an implicit finite difference scheme in combination with the quasi-linearization technique. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the non-uniform slot injection has just the opposite effect. An increase of rotation and total enthalpy at the wall causes separation to occur earlier while cooling delays it. An increase of the Mach number shifts the point of separation upstream due to the adverse pressure gradient. The non-uniform total enthalpy at the wall has a very little effect on the skin friction and hence on the point of separation.
9 citations
TL;DR: In this paper, the effects of non-uniform multiple slot injection (suction) and nonuniform wall enthalpy on the steady nonsimilar compressible laminar boundary-layer flow over a two-dimensional and axisymmetric bodies were investigated.
Abstract: An analysis is performed to study the effects of nonuniform multiple slot injection (suction) and nonuniform wall enthalpy on the steady nonsimilar compressible laminar boundary-layer flow over a two-dimensional and axisymmetric bodies. Nonsimilar solution is obtained from the origin of the stream-wise coordinate to the exact point of separation. The difficulties arising out at the starting point of the streamwise coordinate, at the edges of the slots and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step sizes along the streamwise direction. It is found that the nonuniform multiple slot injection moves the point of separation downstream but the nonuniform multiple slot suction has the reverse effect. Also, separation can be delayed more effectively by applying nonuniform multiple slot injection as compared to the nonuniform single slot injection. The nonuniform total enthalpy at the wall (i.e., the cooling or heating of the wall in the slots) along the streamwise coordinate has very little effect on the skin friction and thus on the point of separation.
7 citations
TL;DR: In this article, the steady nonsimilar compressible laminar boundary-layer flow over a yawed infinite circular cylinder with non-uniform slot injection (suction) has been studied up to the point of separation.
Abstract: The steady nonsimilar compressible laminar boundary-layer flow over a yawed infinite circular cylinder with nonuniform slot injection (suction) has been studied up to the point of separation. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) are removed by choosing appropriate nonuniform mass transfer distributions in the slot. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is found that the nonuniform slot injection moves the point of separation downstream but the nonuniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The yaw angle has very little effect on the location of the point of separation.
6 citations
References
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Book•
01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
5,562 citations
Book•
30 Nov 1961
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.
5,317 citations
Book•
28 Mar 1988TL;DR: In this article, a comprehensive presentation of numerical methods suitable for the analysis of various heat transverse and fluid flow problems that occur in research, practice, and university instruction is given.
Abstract: A comprehensive presentation is given of virtually all numerical methods that are suitable for the analysis of the various heat transverse and fluid flow problems that occur in research, practice, and university instruction. After reviewing basic methodologies, the following topics are covered: finite difference and finite element methods for parabolic, elliptic, and hyperbolic systems; a comparative appraisal of finite difference versus finite element methods; integral and integrodifferential systems; perturbation methods; Monte Carlo methods; finite analytic methods; moving boundary problems; inverse problems; graphical display methods; grid generation methods; and programing methods for supercomputers.
718 citations
TL;DR: In this article, a new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented, which is of the same type as those encountered in the treatment of similarity boundary layers.
Abstract: A new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented. The governing equations generated by the local nonsimilarity solution method are of the same type as those encountered in the treatment of similarity boundary layers. In addition to its local applicability, the utility of the new method is enhanced by its simplicity and directness, both in concept and in actual computations. Several nonsimilar velocity boundarylayer problems are solved herein with a view to illustrating the method, the participating nonsimilarities stemming from the freestream velocity distribution, surface mass transfer, and transverse curvature. On the basis of comparisons with available published information as well as of comparisons internal to the method itself, it may be concluded that the local nonsimilarity method provides results of high accuracy at all streamwise locations, except those near a point of separation.
243 citations
"Non-uniform slot injection (suction..." refers background or methods in this paper
...The reason for this difference is the neglection [ 2 ], [3] of the derivatives of certain terms on the right hand side of the Eqs....
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...The skin friction and heat transfer parameters ((F,)~, (G,),~) have been compared with those of the differential-difference method [5], [6], local nonsimilarity method [ 2 ], asymptotic method [3], [4], momentum integral method [7], and finite difference method [9]....
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...Since then there have been several studies pertaining to nonsimilar flow over two-dimensional and axisymmetric bodies both by approximate and exact methods such as local nonsimilarity method [ 2 ], asymptotic method [3], [4], differential-difference method [5], [6], momentum integral method [7] and finite difference method [8], [9]....
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