# Nonuniform slot injection (suction) into a compressible flow

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.

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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

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TL;DR: The results show that the flow is influenced by the combined effect of radiation and localized suction, which moves the separation point downstream, towards the plate's end, and increases total drag.

Abstract: The effects of thermal radiation and localized suction on the steady turbulent compressible boundary layer flow with adverse pressure gradient are numerically studied. The compressible flow is subjected to a constant localized suction velocity and the fluid is considered as a radiative optically thin gray fluid. The plate is adiabatic and the flow is subjected to adverse pressure gradient.The Reynolds Averaged Boundary Layer (RABL) equations with appropriate boundary conditions are transformed using the compressible Falkner Skan transformation. The resulting nonlinear, coupled system of partial differential equations (PDEs) is solved using the Keller box method. For the eddy kinematic viscosity, the turbulent models of Cebeci Smith and Baldwin Lomax are employed. For the turbulent Prandtl number, the extended Kays Crawford model is used. The obtained results are validated with previously published computational results and with experimentally based correlations, showing a good agreement.The results show that the flow is influenced by the combined effect of radiation and localized suction. The coupled effect moves the separation point downstream, towards the plate's end, and increases total drag. Radiation alters the thermal boundary layer above the plate by cooling the fluid at plate's vicinity and by slightly increasing the boundary layer maximum temperature.

8 citations

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TL;DR: In this paper, the effects of the magnetic field and localized suction on the steady turbulent compressible boundary-layer flow with adverse pressure gradient are numerically studied, and the resulting coupled and nonlinear system of PDEs is solved using the Keller's box method.

Abstract: The effects of the magnetic field and localized suction on the steady turbulent compressible boundary-layer flow with adverse pressure gradient are numerically studied. The magnetic field is constant and applied transversely to the direction of the flow (global or local). The fluid flow is subjected to a constant velocity of localized suction, and there is no heat transfer between the fluid and the plate (adiabatic plate). The Reynolds-Averaged Boundary-Layer (RABL) equations and their boundary conditions are transformed using the compressible Falkner-Skan transformation. The resulting coupled and nonlinear system of PDEs is solved using the Keller’s box method. For the eddy-kinematic viscosity the turbulent models of Cebeci-Smith and Baldwin-Lomax are employed. For the turbulent Prandtl number the extended Kays-Crawford’s model is used. The flow is subjected to an adverse pressure gradient. The obtained results show that the flow field can be controlled by the applied magnetic field as well as by localized suction.

7 citations

### Cites background from "Nonuniform slot injection (suction)..."

...The combined influence of localized injection and localized suction retains the boundary-layer flow, reducing skin friction [8], [9]....

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TL;DR: In this paper, the steady, compressible, turbulent boundary-layer flow, with heat and mass transfer, over a wedge, is numerically studied, where the fluid is considered to be a Newtonian ideal gas (air) and it is subject to a constant velocity of suction/injection applied globally or locally to the wedge.

Abstract: The steady, compressible, turbulent boundary-layer flow, with heat and mass transfer, over a wedge, is numerically studied. The fluid is considered to be a Newtonian ideal gas (air) and it is subject to a constant velocity of suction/injection applied globally or locally to the wedge. The Reynolds-Averaged Boundary-Layer (RABL) equations and their boundary conditions are transformed using the compressible Falkner–Skan transformation. The resulting coupled and nonlinear system of PDEs is solved using the Keller-box method. For the eddy-kinematic viscosity the Cebeci–Smith and Baldwin–Lomax turbulent models are employed. For the turbulent Prandtl number the extended model of Kays–Crawford is used. Numerical calculations are carried out for the case of an adiabatic, cooled or heated wall and for different values of the parameters of the problem under consideration. The obtained results show that the flow field can be controlled by the suction/injection velocity and it is influenced by the dimensionless pressure parameter m .

4 citations

### Cites background from "Nonuniform slot injection (suction)..."

...The combined influence of localized injection and localized suction retains the boundary-layer flow, reducing skin friction [11], [12]....

[...]

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TL;DR: In this paper, the combined effect of magnetic field, thermal radiation and local suction on the steady turbulent compressible boundary layer flow with adverse pressure gradient is numerically studied, where the magnetic field is constant and applied transversely to the direction of the flow.

Abstract: The combined effect of magnetic field, thermal radiation and local suction on the steady turbulent compressible boundary layer flow with adverse pressure gradient is numerically studied. The magnetic field is constant and applied transversely to the direction of the flow. The fluid is subjected to a localized suction and is considered as a radiative optically thin gray fluid. The Reynolds Averaged Boundary Layer (RABL) equations with appropriate boundary conditions are transformed using the compressible Falkner Skan transformation. The nonlinear and coupled system of partial differential equations (PDEs) is solved using the Keller box method. For the eddy-kinematic viscosity the Baldwin Lomax turbulent model and for the turbulent Prandtl number the extended Kays Crawford model are used. The numerical results show that the flow field can be controlled by the combined effect of the applied magnetic field, thermal radiation, and localized suction, moving the separation point, xs , downstream towards the plate’s end, and increasing total drag, D . The combined effect of thermal radiation and magnetic field has a cooling effect on the fluid at the wall vicinity. The combined effect has a greater influence in the case of high free-stream temperature.

3 citations

### Cites background from "Nonuniform slot injection (suction)..."

...The combined influence of localized injection and localized suction retains the boundary layer flow, reducing skin friction [36]....

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##### References

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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

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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

30 Nov 1955

TL;DR: In this article, a generalized concept of flow separation is presented and the conditions in the neighbourhood of a line of separation are deduced and the resulting flow is shown to be composed of two basic elements (i) the free vortex layer and (ii) the bubble each of which is identified by a characteristic pattern formed in the solid surface by the family of limiting streamlines.

Abstract: A generalized concept of flow separation is presented. and the conditions in the neighbourhood of a line of separation are deduced. The resulting flow is shown to be composed of two basic elements (i) the free vortex layer and (ii) the bubble each of which is identified by a characteristic pattern formed in the solid surface by the family of limiting streamlines. From the results of the analysis the physical structures of possible three-dimensional flows are readily inferred.

156 citations

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01 Jan 1976

TL;DR: The Diffusion Equation as discussed by the authors is a generalization of the Wave Equation, which is used in the Laplace Transform Methods (LTLM) and Green's Functions.

Abstract: The Diffusion Equation. Laplace Transform Methods. The Wave Equation. The Potential Equation. Classification of Second Order Equations. First Order Equations. Extensions. Perturbations. Green's Functions. Variational Methods. Eigenvalue Problems. More on First Order Equations. More on Characteristics. Finite-Difference Equations and Numerical Methods. More on Transforms. Singular Perturbation Methods. Index.

154 citations