Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is com...Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation(DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the eNmethod to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it;local heating always slightly promotes the transition.Finally, recommendations are given for practical engineering applications based on the present results.展开更多
The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the lin...The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.展开更多
By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on th...By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting （T-S） waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.展开更多
In this paper, the differences of turbulent coherent structure beween the smooth and rough boundary lavers are analysed.Based on the discussing the transient properties from the smooth wall tothe rough wall,the physic...In this paper, the differences of turbulent coherent structure beween the smooth and rough boundary lavers are analysed.Based on the discussing the transient properties from the smooth wall tothe rough wall,the physicalmodel of coherent structure for the rough boundary layer are established.The width of slwly-moving turbulent spot and the bursting time are obtained,which are in agreement with experimental results.展开更多
Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dyna...Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dynamics （CFD） are reviewed and some subjects worthy to be studied are pro- posed in this paper. The flow-field and motion law of ISF, mathematics definition of strong viscous shear layer flow in ISF, ISF equations, wall-surface compatibility criteria （Gao＇s criteria ）, space scale variety law of strong viscous shear layer reveals flow mechanism and local space small scale triggered by strong interaction that cause some abnormal severe local pneumatic heating phenomenon in hypersonic flow. Gao＇s ISF theory was used in near wall flow, free ISF flow simulation and design of computing grids, Gao＇s wall-surface criteria were used to verify calculation reliability and accuracy of near wall flows, ISF theory approximate analytical result of shock waves-boundary layer interac- tion and ISF equations were used to obtain the numerical exact solution of local area flow （ such as stationary point flow）. Some new subjects, such as, improving near-wall turbulent models according to the turbulent flow simulation satisfying the wall-criteria and illustrating relation between grid-con- vergence based on the wall criteria and other convergence tactics, are suggested. The necessity of applying Gao＇s ISF theory and wall criteria is revealed. Difficulties and importance of hypersonic vis- cous/in-viscid interaction phenomenon were also emphasized.展开更多
A theoretical model is developed using statistical rate theory to determine the rate of molecular transport across the interface of a growing spherical zeolite crystal. The model is expressed in terms of the interface...A theoretical model is developed using statistical rate theory to determine the rate of molecular transport across the interface of a growing spherical zeolite crystal. The model is expressed in terms of the interface concentration. Two model constants appear in the expression for the equilibrium exchange rate. In order to validate the model, zeolite crystallization is investigated for a system for which experimental data exist. The model constants were first established using the measured growth rates at a specific temperature. Then the model was used to predict the growth rate at other temperatures.展开更多
Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which t...Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.展开更多
A 1-dimensional K-model parameterized by the local similarity theory is used to study the structure of the stably stratified boundary layer. The computed results are quite consistent with those of the second-order mom...A 1-dimensional K-model parameterized by the local similarity theory is used to study the structure of the stably stratified boundary layer. The computed results are quite consistent with those of the second-order moments model. Thus, the model can be used to improve the simulated results and the parameterized accuracy.展开更多
The equation arising from Prandtl boundary layer theory (e)u/(e)t-(e)/(e)x1(a(u,x,t)(e)u/(e)xi)-fi(x)Diu+c(x,t)u=g(x,t)is considered.The existence of the entropy solution can be proved by BV estimate method.The intere...The equation arising from Prandtl boundary layer theory (e)u/(e)t-(e)/(e)x1(a(u,x,t)(e)u/(e)xi)-fi(x)Diu+c(x,t)u=g(x,t)is considered.The existence of the entropy solution can be proved by BV estimate method.The interesting problem is that,since a(·,x,t) may be degenerate on the boundary,the usual boundary value condition may be overdetermined.Accordingly,only dependent on a partial boundary value condition,the stability of solutions can be expected.This expectation is turned to reality by Kru(z)kov's bi-variables method,a reasonable partial boundary value condition matching up with the equation is found first time.Moreover,if axi(·,x,t)|x∈(e)Ω=a(·,x,t)|x∈(e)Ω=0 and fi(x)|x∈(e)Ω=0,the stability can be proved even without any boundary value condition.展开更多
基金supported the National Natural Science Foundation of China (Grant No. 92271102)。
文摘Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation(DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the eNmethod to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it;local heating always slightly promotes the transition.Finally, recommendations are given for practical engineering applications based on the present results.
基金Project supported by the National Key Research and Development(R&D)Program of China(No.2016YFA0401200)the National Natural Science Foundation of China(Nos.11402167,11332007,11672204,11672205,and 11732011)
文摘The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.
基金Project supported by the National Natural Science Foundation of China(No.10872018)
文摘By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting （T-S） waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.
文摘In this paper, the differences of turbulent coherent structure beween the smooth and rough boundary lavers are analysed.Based on the discussing the transient properties from the smooth wall tothe rough wall,the physicalmodel of coherent structure for the rough boundary layer are established.The width of slwly-moving turbulent spot and the bursting time are obtained,which are in agreement with experimental results.
基金Supported by the National Natural Science Foundation(10702009)
文摘Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dynamics （CFD） are reviewed and some subjects worthy to be studied are pro- posed in this paper. The flow-field and motion law of ISF, mathematics definition of strong viscous shear layer flow in ISF, ISF equations, wall-surface compatibility criteria （Gao＇s criteria ）, space scale variety law of strong viscous shear layer reveals flow mechanism and local space small scale triggered by strong interaction that cause some abnormal severe local pneumatic heating phenomenon in hypersonic flow. Gao＇s ISF theory was used in near wall flow, free ISF flow simulation and design of computing grids, Gao＇s wall-surface criteria were used to verify calculation reliability and accuracy of near wall flows, ISF theory approximate analytical result of shock waves-boundary layer interac- tion and ISF equations were used to obtain the numerical exact solution of local area flow （ such as stationary point flow）. Some new subjects, such as, improving near-wall turbulent models according to the turbulent flow simulation satisfying the wall-criteria and illustrating relation between grid-con- vergence based on the wall criteria and other convergence tactics, are suggested. The necessity of applying Gao＇s ISF theory and wall criteria is revealed. Difficulties and importance of hypersonic vis- cous/in-viscid interaction phenomenon were also emphasized.
文摘A theoretical model is developed using statistical rate theory to determine the rate of molecular transport across the interface of a growing spherical zeolite crystal. The model is expressed in terms of the interface concentration. Two model constants appear in the expression for the equilibrium exchange rate. In order to validate the model, zeolite crystallization is investigated for a system for which experimental data exist. The model constants were first established using the measured growth rates at a specific temperature. Then the model was used to predict the growth rate at other temperatures.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002098 and 11332007)
文摘Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.
文摘A 1-dimensional K-model parameterized by the local similarity theory is used to study the structure of the stably stratified boundary layer. The computed results are quite consistent with those of the second-order moments model. Thus, the model can be used to improve the simulated results and the parameterized accuracy.
基金The paper is supported by Natural Science Foundation of Fujian province(2019J01858)supported by SF of Xiamen University of Technology,China.The author would like to think reviewers for their good comments.
文摘The equation arising from Prandtl boundary layer theory (e)u/(e)t-(e)/(e)x1(a(u,x,t)(e)u/(e)xi)-fi(x)Diu+c(x,t)u=g(x,t)is considered.The existence of the entropy solution can be proved by BV estimate method.The interesting problem is that,since a(·,x,t) may be degenerate on the boundary,the usual boundary value condition may be overdetermined.Accordingly,only dependent on a partial boundary value condition,the stability of solutions can be expected.This expectation is turned to reality by Kru(z)kov's bi-variables method,a reasonable partial boundary value condition matching up with the equation is found first time.Moreover,if axi(·,x,t)|x∈(e)Ω=a(·,x,t)|x∈(e)Ω=0 and fi(x)|x∈(e)Ω=0,the stability can be proved even without any boundary value condition.
