Measurements in the field of a spark excited compressible axisymmetric jet

Acoustic phase (ensemble) averaged measurements were performed in a constant temperature, axisymmetric, Mach 0.6 jet of air. These measurements show that the noise directly radiated by the coherent structure in the jet flow field was responsible for the directivity of the acoustic field.List of symbols D nozzle exit diameter - f frequency, Hz - r radial distance from the jet centerline - SPL sound pressure level (ref.: 20 micro pascals) - St Strouhal number, = f D/U - U jet exit velocity - x distance along the jet axis from the nozzle exit - t time - ensemble average quantity     

Experimental determination of the free-stream disturbance field in a short-duration supersonic wind tunnel

The free-stream disturbance field in a short-duration supersonic wind tunnel is investigated at a nominal Mach number of Ma=2.54. A specially designed constant-temperature anemometer is used to be able to draw a complete fluctuation diagram within one wind tunnel run (testing time: 120 ms). It is shown that the disturbance field is dominated by acoustic waves radiated from the turbulent boundary layer on the nozzle and the sidewalls, like in conventional supersonic wind tunnels. The acoustic field appears to be composed of highly localized shivering Mach waves superimposed on a background of eddy Mach waves.Abbreviations  a constant in the thermal conductivity/temperature power law of air: k/k_r=(T/T_r)^a (dimensionless) - b constant in the viscosity/temperature power law of air: /_r=(T/T_r)^b (dimensionless) - Be bandwidth (Hz) - A, B constants in the wire heat transfer relation (Eq. (7), dimensionless) -   (dimensionless) - c_p specific heat at constant temperature (kJ/kg K) - c_v specific heat at constant volume (kJ/kg K) -  boundary layer thickness (m) - D function of the overheat ratio (dimensionless) - e anemometer output voltage (V) - _F end-loss attenuation factor for mass flow sensitivity (dimensionless) - _G end-loss attenuation factor for total temperature sensitivity (dimensionless) -  recovery factor (dimensionless) - f frequency (Hz) - f₁ normalized frequency (dimensionless) - F anemometer nondimensional sensitivity to mass flow fluctuations (dimensionless) - G anemometer nondimensional sensitivity to total temperature fluctuations (dimensionless) - F_AC F×F (dimensionless) - G_AC G×G (dimensionless) - f,g functions in the wire heat transfer relation (Eq. (7), dimensionless) -  c_p/c_v (dimensionless) - k thermal conductivity of air (W/m K) - k_r thermal conductivity of air at temperature T_r (W/m K) - k anemometer sensitivity to total temperature fluctuations (V/K) - l Mach rhombus half-length (Fig. 1, m) - Ma Mach number (dimensionless) -  viscosity of air (kg/m·s) - _r viscosity of air at temperature T_r (kg/m·s) - n constant in the wire heat transfer relation (Eq. (7), dimensionless) - Nu Nusselt number (dimensionless) - p pressure (Pa) - p₀ stagnation pressure (Pa) - r –F/G (dimensionless) - R unit Reynolds number (1/m) - Re Reynolds number (dimensionless) -  correlation coefficient between mass flow and total temperature fluctuations (dimensionless) -  density (kg/m³) - T time span (s) - T₀ total temperature (K) - T_r reference temperature (K) - T_w hot wire temperature (K) -  overheat ratio: =(T_w–T₀)/T₀ (dimensionless) -  –<e>/G (%) - u x-component of the flow velocity (m/s) - u_s source velocity at acoustic origin (m/s) - u inviscid velocity at acoustic origin (m/s) - x wind tunnel axis (Fig. 1, m)Symbols  x̄ temporal mean value of a fluctuating quantity x - x fluctuating part of x: x=x–x̄ - x_RMS^' root mean square of x - <x> x_RMS^'/x̄ - (X) relative uncertainty of a random variable X

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Experimental investigation of the flow in the mixing layer in the initial section of an underexpanded jet in a parallel stream

The results are given of an experimental investigation of the flow in the initial section of a turbulent underexpanded jet exhausting from a profiled nozzle with Mach number M _a = 2.56 at the exit into a parallel stream with Mach number M = 3.1. Analysis of the results of measurement of the fields of the total head p₀ and the stagnation temperature T₀ in conjunction with results of calculation of a jet of an ideal gas make it possible to construct the velocity profile in the mixing layer of the underexpanded jet in the parallel supersonic flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–163, January–February, 1981.     

Sensitivity of three-segment electrodiffusion probes to eddy shedding

The influence of eddy shedding on the instantaneous readings of a three-segment cylindrical electrodiffusion velocity probe was investigated in an immersed jet with a very low turbulence intensity, = 1.2%. The velocity fluctuations measured by the three-segment probe were smaller than 2.6%, and the maximum error in the flow angle estimation was 2. Vortices with the Strouhal frequency were detected by a simple electrodiffusion probe placed downstream of the three-segment probe, but no peaks with this frequency were found on the frequency spectra of the three-segment probe. From the probe response to a stepwise change of the polarization voltage the characteristic times of the transient process were estimated. List of symbols a parameter in Eq. (1) [A s^b m^-b] - A amplitude gain - b parameter in Eq. (1) - c parameter in Eq. (3) [A s^–1/2] - d probe diameter [m] - f frequency [s^–1] - f _s recording frequency [s^–1] - G power spectrum - I _k relative current through k-th segment, Eq. (2) - i total current [A] - i _k current through k-th segment [A] - N number of data samples - Re Reynolds number, - Sr Strouhal number, - t time [s] - t ₀ characteristic transient time [s] - v jet velocity [m s^-1] - v time mean value of velocity [m s^-1] - v _x, y velocity components measured by probe [m s^-1] - var variance, var - dynamic viscosity [Pa s] - density [kg m^-3] - relative deviation, [%] - flow angle, see Fig. 1 - dimensionless frequency For the financial support of this work we express our thanks to the DFG, Bonn. The assistance of Dr. Ondra Wein and Dr. Pavel Mitschka is greatly appreciated.     

Jet flow field during screech

Measurements were made of the flow field structure and the near field parameters of a jet exhausting from a sonic nozzle with a 1.27 cm exit diameter. Compressed air was used for obtaining stagnation pressures up to 5 atmospheres. The jet exhausted vertically from a settling chamber into an acoustically insulated room and through an insulated duct out through the roof. Measurements were made with several different reflecting surfaces at the nozzle exit as well as an insulating surface. Schlieren pictures at 500,000 frames/s were taken. Overall sound pressure level, impact pressure level downstream, and sound frequency analyzer measurements were made.It was found that with a reflecting surface there was a radial oscillation of the jet which had the same frequency as the dominant sound (screech) frequency emitted by the jet. No axial motion of the inviscid part of the flow structure was detected. The insulated surface at the nozzle exit appeared to shift the dominant frequencies of the sound generated into the region above the audible (>16 KHz). A reflecting surface yielded pure tones (screech) with one or two harmonics. The dominant (screech) frequency decreased as the stagnation pressure increased. The screech frequency was found to be approximately inversely proportional to the length of the first shock cell.Nomenclature C ₀ speed of sound in ambient gas - D diameter of nozzle exit - f frequency of pure tone (screech frequency) - L ₁ length of first cell, distance between nozzle exit plane and intersection of shock with shear layer - M Mach number based on isentropic expansion to ambient pressure - P ₀ stagnation chamber pressure - P _a ambient pressure - P _i impact pressure - R _LB distance from nozzle centerline to left boundary of jet - R _RB distance from nozzle centerline to right boundary of jet - t time - period of screech, 1/f - X _E axial distance of eddy from nozzle exit plane - X _I axial distance of third cell shock intersection from nozzle exit plane - Y _I transverse distance of third cell shock intersection from nozzle centerline     

Heat conduction in a plane wall subject to periodic temperature changes

Analytical solutions for the heat conduction in a plane wall with periodic temperature variations at the wall surface are presented. Series and asymptotic developments of these solutions are deduced. The results are important for the calculation of the heat transfer in rotary kilns or other rotaring units.

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Die Wärmeleitung in einer ebenen Wand mit periodischen Temperaturänderungen

Zusammenfassung Es werden analytische Lösungen für die Wärmeleitung in einer ebenen Wand mit periodischen Temperaturänderungen an ihrer Oberfläche mitgeteilt. Reihen- und asymptotische Entwicklungen dieser Lösungen werden abgeleitet. Die Ergebnisse sind wichtig für die Berechnung des Wärmetransportes in Drehrohröfen oder ähnlichen Maschinen.

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Nomenclature a ² =/ C m²/s thermal diffusivity, Eq. (1) - C J/kg K specific heat - F K initial temperature of the wall, Eq. (4) - F m² surface of the wall - G Green's function, Eq. (10) - G₁ Green's function, Eq. (12) - h m thickness of the wall - H Heaviside function, Eq. (5) - k constant, Eq. (25) - k _x constant, Eq. (25) - Q J total energy, Eq. (17) - Q ^u J total energy from temperatureU, Eq. (18) - Q ^v J total energy from temperatureV, Eq. (19) - s s^–1 Laplace variable - t s time - t ₁ s heating time, Eq. (5) - t ₂ s period, Eq. (5) - T K temperature of the wall - T _i K surface temperature of the wall - T ₁ K surface temperature of the wall during the heating time - T ₂ K surface temperature of the wall during the cooling time - U K temperature of the wall defined in problem 1 - V, K temperature of the wall defined in problem 2 - x m coordinate - ₀ W/m²K overall heat transfer coefficient, Eq. (31) - ₁₀ W/m² K overall heat transfer coefficient, Eq. (32) - ₂₀ W/m² K overall heat transfer coefficient, Eq. (33) - Dirac Delta function - s^–1/2 parameter, Eq. (6) - W/mK thermal conductivity - kg/m³ specific mass - dimensionless time, Eq. (34) - Riemann Zeta function surfix Laplace transformed variable     

Physical properties of the flow in the separation region for three-dimensional interaction of a boundary layer with a shock wave

In a supersonic stream we consider the three-dimensional flow in the plane of symmetry in the region of interaction of a boundary layer with a shock wave which arises ahead of an obstacle mounted on a plate. The principal characteristic of this flow is the penetration of a filament of the ideal fluid within the separation zone and the formation on the surface of the plate and obstacle of narrow segments with high pressures, high velocity gradients, and large heat transfer coefficients.Pressure distribution measurements were made, shadow and schlieren photos were taken, and photographs of the flow pattern on the surface were made using dye coatings and low-melting models. The basic physical characteristics of the separation flow are established. The independence of the separation zone length of the boundary layer thickness is shown. Local supersonic flows are detected in the separation region, flow regimes are identified as a function of the angle of encounter of the separating flow with the obstacles, characteristic flow zones in the interaction region are identified.Notation s coordinate of separation point on the plate - l length of separation zone - H obstacle height - d obstacle transverse dimension - u freestream velocity - velocity gradient on stagnation line of obstacle - b jet width - compression shock standoff from the body - p static pressure - p_* pressure at stagnation point on obstacle - density - viscosity coefficient - boundary-layer thickness - compression shock angle - effective angle of separation zone - setting angle of obstacle on plate - M Mach number - R Reynolds number - P Prandtl number     

Outflow of an unexpanded jet into counter supersonic and subsonic flows

The article gives the results of an experimental investigation of the geometric structure of an opposing unexpanded jet. It discusses flow conditions with interaction between the jet and sub- and supersonic flows. It is shown that, with the outflow of an unexpanded jet counter to a supersonic flow, there are unstable flow conditions. For stable flow conditions with one roll, dependences are proposed determining the form of a jet in a supersonic opposing flow. A generalized dependence is obtained for the distribution of the pressure at the surface of a body with a jet, flowing out counter to a subsonic flow. The range of change in the determining parameters are the following: Mach numbers at outlet cross section of nozzle, M _a = 1 and 3; Mach numbers of opposing flow, M = 0.6–0.9 and 2.9; degree of effectiveness of jet, n = p _a /p = 0.5–800 (p _a and p are the static pressures at the outlet cross section of the nozzle and in the opposing flow); the ratios of the specific heat capacities, _a = = 1.4; the drag temperatures of the jet and the flow, T_o = T_oa = 290°K.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 89–96, January–February, 1977.     

Cryogenic transonic wind tunnels and the condensation of nitrogen

A brief tutorial on the need for Reynolds number similarity and the advent of cryogenic transonic wind tunnels is presented. Experimental results of nitrogen condensation in nozzles are collected and related to the flow in the wind tunnels. New theoretical approaches to a solution of the condensation problem in the supersaturated state are proposed.List of symbols a speed of sound - A area - {ovc} wing area/wing span - c _p pressure coefficient, Eq. (12) - G ^* energy of formation of a critical droplet, Eq. (14) - h altitude - J homogeneous nucleation rate, Eq. (13) - k Boltzmann constant - l characteristic length - M Mach number, Eq. (2) - n ^* number of molecules in a critical droplet, Eq. (14) - p static pressure - p ₀ wind tunnel supply pressure - p ⁰ standard pressure - p equilibrium vapor pressure - P wind tunnel fan power - q dynamic pressure - Re Reynolds number, Eq. (1) - t time - T temperature - T ₀ wind tunnel supply temperature - molecular volume - V air speed - ratio of specific heats - dynamic viscosity - v kinematic viscosity - density - surface tension This paper is dedicated to my old friend Eberhard Berger upon his retirement from the Föttinger Institut of the Technical University of Berlin     

Experimental investigation into the effect of heat transfer on compressible air stream in a duct

A converging nozzle-constant area parallel passage with an outer duct encasing the constant-area passage has been built for investigating the effect of heat transfer on subsonic flow of an air stream. It is concluded experimentally as can be predicted analytically that large quantities of heat are needed in order to accelerate very slow air stream (incompressible) to sonic conditions. It is observed experimentally as confirmed analytically, that the increase in Mach number with heat addition is associated with a decrease in the local static pressure along the axis of the duct. It could be concluded that any more heat added beyond thermal choking will be accompanied by a decrease in the mass flow rate of the compressible flowing air.Nomenclature A cross-sectional area of the duct - C _{P air} specific heat of air joules/kg. °K - C _d discharge coefficient - D duct diameter - d orifice diameter m - dA _d elemental lateral area of the duct - h overall heat transfer coefficient - h head across orifice, mm. - M Mach number - m _air mass flow rate of air - P local static pressure - P _b back pressure at duct outlet - P ₀₁ stagnation pressure at duct inlet - gas density - _u air density upstream of orifice - _q incremental heat flow - T local static temperature - T ₀₁ stagnation temperature at duct inlet - T _h hot water temperature - q heat added per kg of flowing air - V flow speed     

Two-point laser Doppler velocimetry measurements in a Mach 1.2 cold supersonic jet for statistical aeroacoustic source model

Single and multi-point laser Doppler velocimetry measurements performed in a cold Mach 1.2 jet flow are used to assess those properties of the aerodynamic field most relevant in the generation of turbulence mixing noise. Single point measurements yield mean velocity profiles, turbulence intensity profiles and power spectral densities of both the velocity and Reynolds stress fields at seven axial stations between the jet exit and the end of the potential core. The longitudinal components of the second-order and fourth-order two-point velocity correlation tensor are obtained from a series of multi-point LDV measurements, whence a cartography of integral space and time scales, convection velocities and acoustic compactness is effected. These results are used to examine differences between subsonic and supersonic jet aerodynamics in terms of their sound generating potential. Finally analytical expressions are proposed for the spatial and temporal parts of the longitudinal correlation coefficient function. These are scaled using the integral space and time scales of the velocity and Reynolds stress fields, and excellent agreement is found with experimentally determined functions.Nomenclature  c_o  Sound speed - D  Exit nozzle diameter - f, f  Spatial correlation function - g, g  Temporal correlation function - f_St  Frequency based Strouhal number - _i  2nd-order integral length scales in i-th direction -  4th-order integral length scales in i-th direction - M_c  Convective Mach number - M_j Jet exit Mach number - q Quantity q evaluated at location y into the flow -  Time average of the quantity q - r Radial distance from the jet exit - r_0.5  Radial location of the shear layer axis - r* Normalised radial coordinate - r_ij Second-order velocity correlation - r_ijkl Fourth-order velocity correlation - St Jet Strouhal number - U_c Convective velocity - U_e Subsonic coflow velocity - U_j Jet exit velocity - U_i Mean part of u_i - u_i Local velocity in i-th direction - u_ti Fluctuating part of u_i - x Distance from the exit nozzle - y Location test point - _i Variance of the velocity component u_i - _ij Variance of the velocity product u_iu_j -  Constant value - _ij Kronecker delta - _c Shear layer thickness - t_i Interarrival time between two ldv samples -  Separation distance in the moving pattern (components _i ) -  Polynomial function -  Separation distance in the fixed pattern (components _i ) -  Time delay -  2nd-order time scale in the fixed pattern -  2nd-order time scale in the moving pattern -  4th-order time scale in the fixed pattern -  4th-order time scale in the moving pattern -  Typical radian frequency where

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Swirling flows in circular-to-rectangular transition ducts

Miniature axisymmetric supersonic nozzles were produced with exit Mach numbers ranging from 1.0 to 2.8 by forming Pyrex^® capillary tubing of 0.6 and 1.2 mm inside diameter into converging-diverging channels. The nozzle contours were measured and were found to compare favorably to ideal solutions given by the axisymmetric method of characteristics. In addition, the surfaces of these nozzles were quite smooth, providing featureless flows at perfect expansion. Schlieren visualization and pitot pressure measurements of the resulting microjets were compared to the literature available for jets produced by larger-scale nozzles. A postponed transition to turbulence is noted in these microjets due to their low Reynolds number. The pitot pressure on centerline is nearly uniform at perfect expansion over core lengths up to 12 nozzle exit diameters. Supersonic microjet nozzles thus provide a more effective small-scale high-pressure gas delivery device than do sonic nozzles of comparable scale at equivalent mass flow rates. Supersonic microjets may therefore have several industrial applications.List of symbols ^* boundary layer displacement thickness, mm - d diameter of nozzle exit, mm - L length of nozzle diverging section, mm - L _c inviscid core length, mm - L _s supersonic region length, mm - M _c convective Mach number - M _e exit Mach number - P _b backpressure at nozzle exit, (equal to ambient pressure in this experiment) - P _e exit pressure of the supersonic jet - P _be exit pressure ratio (P _b /P _e ) - P _p impingement pressure (pitot pressure) - P ₀ stagnation pressure supplied to nozzle - P _n overall pressure ratio (P ₀/P _b ,) - r radial dimension (cylindrical coordinate system), mm - r ₀ radius of throat, mm - Re _d Reynolds number, based on nozzle exit diameter - V _e exit velocity, m/s - x axial dimension (cylindrical coordinate system), mm This research was sponsored by National Science Foundation Grant DMI 9400119, as part of a study of the assist-gas dynamics of laser cutting.     

Treatment of moisture condensation on fins

An analysis of natural convection from a vertical plate fin when the fin base temperature is below the dew point of the surrounding air is presented in this paper. The analytical solution derived is based upon a constant heat and mass transfer coefficient and is also valid for forced convection. The results of this simplified theory are compared with a numerical solution where the coupling of convection and conduction is taken into account. An experimental verification of the results is also shown.

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Aus Kondensation von Feuchtigkeit an Rippen

Zusammenfassung Es wird eine Analyse der freien Konvektion an einer vertikalen plattenförmigen Rippe dargestellt, bei der die Temperatur im Anfangsbereich der Rippe unterhalb des Taupunktes der umgebenden Luft liegt. Die abgeleitete analytische Lösung beruht auf einem konstanten Wärme- und Stoffübergangskoeffizienten und gilt auch für die erzwungene Konvektion. Die Resultate dieser vereinfachten Theorie werden mit einer numerischen Lösung verglichen, in der die Verbindung von Konvektion und Wärmeleitung in Betracht gezogen wird. Angeführt wird auch eine experimentelle Bestätigung der Resultate.

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Nomenclature a _f thermal diffusivity of air - A, B constants in Eq. (7) - c constant defined in Eq. (3) - D diffusion coefficient - f an arbitrary function ofT andx in Eq. (12) - F ₁,F ₂ coefficients in differential Eq. (13) - g gravitational acceleration - h heat transfer coefficient - h _m mass transfer coefficient - k thermal conductivity of fin - k _f thermal conductivity of air - l latent heat of moisture condensation - L total length of fin - L _w length of wet fin - m parameter, (h/kt)^1/2 - m _l dimensionless parameter, 1+ B/T _r - m _y parameter,m m _l ^1/2 - p pressure of surrounding air - p _ws saturation pressure of water vapor - p _w partial pressure of water vapor in air - Pr Prandtl number,/a _f - q total heat fluxl - q _c convective heat flux - q _m heat flux - q _r radiative heat flux - R parameter in Eq. (14) - R _w specific gas constant of water vapor - t half thickness of fin - T temperature - T _b base temperature of wet fin - T _c base temperature of dry fin=saturation temp. of vapor - T _r reference temperature defined in Eq. (15) - T temperature of surrounding air - T temp, difference between fin surface and surroundings - v initial temperature for quasilinearization - x vertical coordinate, see Fig. 1 - y horizontal coordinate, see Fig. 1 - coefficient of thermal expansion - emissivity - dimensionless parameter in Eq. (14) - ø _d heat flux of dry fin - ø _tot total heat flux of dry-wet fin - kinematic viscosity - Stefan-Boltzman coefficient - relative humidity of air     

Diabatic internal source flow

Summary A study is made of diabatic internal source flow. It is shown that for such a flow self similar solutions to the full equations of motion are possible provided that the transport properties ( and k) are assumed constant. Solutions are presented for several cases representing internal heat generation in a confined supersonic flow.Nomenclature a, b, c, d, e constant exponents - f dimensionless velocity - F dimensionless velocity - g dimensionless temperature - G dimensionless temperature - H ₀ stagnation enthalpy - h dimensionless pressure - k thermal conductivity - M Mach number - M _c centerline Mach number - m dimensionless density - n dimensionless internal heat strength - Pr Prandtl number - p pressure - Q dimensionless internal heat source parameter - strength of internal heat source - R gas constant - Re Reynolds number - r radial coordinate - T temperature - u radial velocity - v tangential velocity - ratio of specific heats - tangential coordinate - coefficient of viscosity - density     

Prediction of stagnation point heat transfer for a slot jet impinging on a concave semicylindrical surface

A systematic procedure has been laid out for assessment of fluid flow and heat transfer parameters for a slot jet impinging on a concave semicylindrical surface. Based on Walz's modifications of the Karman-Pohlhausen integral method, expressions have been derived for evaluation of the momentum thickness, boundary layer thickness and the displacement thickness at the stagnation point. The work then has been extended for the estimation of thermal boundary layer thickness and local heat transfer coefficients. A correlation has been presented for the Nusselt number at the stagnation point as a function of the Reynolds number for different non-dimensional distances from the exit plane of the jet to the impingement surface.

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Berechnung des Wärmeübergangs im Staupunkt eines Strahles, der aus einer rechteckigen öffnung auf eine konkave halbzylindrische Fläche auftrifft

Zusammenfassung Es wurde eine systematische Prozedur für die Abschätzung von Strömungs- und Wärmeübergangsparametern für einen Strahl, der auf eine konkave halbzylindrische Fläche auftrifft, aufgestellt. Basierend auf Walz's Modifikationen der Karman-Pohlhausen Integral-Methode, wurden Ausdrücke für die Berechnung der Impulsdicke, der Grenzschichtdicke und die Versetzungsdicke am Staupunkt abgeleitet. Die Arbeit wurde dann auf die Abschätzung der thermischen Grenzschichtdicke und der lokalen Wärmeübertragungskoeffizienten ausgedehnt. Es wird eine Beziehung für die Nusselt-Zahl am Staupunkt als eine Funktion der Reynolds-Zahl für verschiedene dimensionslose Abstände von der Austrittsfläche des Schlitzes bis zur Aufprallfläche aufgestellt.

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Nomenclature c _p specific heat at constant pressure - h ₀ heat transfer coefficient at the stagnation point - H distance from the exit plane of the jet to the impingement surface - k thermal conductivity - Nu _.5 Nusselt number based on impinging jet quantities =h _0.50/k - Nu _.5,0 stagnation point Nusselt number =h _{0 0.50}/k - p pressure - p _a ambient pressure - p ₀ maximum pressure or stagnation pressure - p(x) static pressure at a distancex from the stagnation point - p(x*) static pressure at nondimensional distancex* from the stagnation point - Re _J jet Reynolds number =U _J W/ - Re _0.5 Reynolds number based on impinging jet quantities =u _{m0 0.50}/ - T temperature - T* nondimensional temperature =(T–T _W)/(T _J–T _W) - T _a room temperature - T _J jet temperature - T _W wall temperature - u velocity component inx andx directions - u _m jet centerline (or maximum) free jet velocity: external (or maximum) boundary layer velocity aty = _m - u _m0 arrival velocity defined as the maximum velocity the free jet would have at the plane of impingement if the plane were not there - U _J jet exit velocity - W jet nozzle width - x* nondimensional coordinate starting at the stagnation point =x/2 _0.50 - x, y rectangular cartesian coordinates - y coordinate normal to the wall and starting at the wall - ratio of thermal to velocity boundary layer thickness = _T/ _m - ₀ ratio of thermal to velocity boundary layer thickness at the stagnation point - * inner layer displacement thickness - _.50 jet half width at the plane of impingement if the plate were not there - d_.5 free jet (half width) thickness whereu=u _m/2 - _m inner boundary layer thickness atu =u _m - _T thermal boundary layer thickness - nondimensional coordinate normal to wall =y/ _m - _T nondimensional coordinate normal to wall =y/ _T - Pohlhausen's form parameter - dynamic viscosity - kinematic viscosity = / - fluid density - momentum thickness - ₀ momentum thickness at the stagnation point